Добавил:

Upload Опубликованный материал нарушает ваши авторские права? Сообщите нам.

Вуз:

Московский государственный индустриальный университет

Предмет:

[НЕСОРТИРОВАННОЕ]

Файл:

basic mathematics for college students.pdf

Скачиваний:

147

Добавлен:

10.06.2015

Размер:

15.55 Mб

Скачать

☆

<<< < Предыдущая 34 35 36 37 38 39 40 41 42 43 44 4546 / 6746 47 48 49 50 51 52 53 54 55 56 57 58 > Следующая >>>

88.SALES TAX The state sales tax rate in Kansas is 5.3%. Estimate the sales tax on a purchase of $596.

89.VOTING On election day, 48% of the 6,200 workers at the polls were volunteers. How many volunteers helped with the election?

90.BUDGETS Each department at a college was asked to cut its budget by 21%. By how much money should the mathematics department budget be reduced if it is currently $4,715?

WRITING

91.Explain why 200% of a number is twice the number.

92.If you know 10% of a number, explain how you can ﬁnd 30% of the same number.

6.5 Interest

559

93.If you know 10% of a number, explain how you can ﬁnd 5% of the same number.

94.Explain why 25% of a number is the same as 14 of the number.

REVIEW

Perform each operation and simplify, if possible.

95. a.	5		1	b.	5	1
95. a.	6		2	b.	6	2
c.	5	1		d.	5	1

	6	2			6	2


96. a.	7			7	b.	7	7
	15		18			15	18
c.	7		7		d.	7	7
	15	18				15	18

S E C T I O N 6.5

Interest

When money is borrowed, the lender expects to be paid back the amount of the loan plus an additional charge for the use of the money. The additional charge is called interest. When money is deposited in a bank, the depositor is paid for the use of the money.The money the deposit earns is also called interest. In general, interest is money that is paid for the use of money.

1 Calculate simple interest.

Interest is calculated in one of two ways: either as simple interest or as compound interest. We begin by discussing simple interest. First, we need to introduce some key terms associated with borrowing or lending money.

•Principal: the amount of money that is invested, deposited, loaned, or borrowed.

•Interest rate: a percent that is used to calculate the amount of interest to be paid. The interest rate is assumed to be per year (annual interest) unless otherwise stated.

•Time: the length of time that the money is invested, deposited, or borrowed.

The amount of interest to be paid depends on the principal, the rate, and the time. That is why all three are usually mentioned in advertisements for bank accounts, investments, and loans, as shown below.

Our

Accounts	$5,000	Principal		$100,000

Rise to	minimum		Home Loan

New	4.75%	Rate		6.375%
New	4.75%	Rate		6.375%
Heights	Time: 13	Time		30-year fixed	Serving the
	Time: 13	Time		30-year fixed	Serving the
COUNTY NATIONAL	months		Foothill		community for over
COUNTY NATIONAL	months		Foothill		community for over
BANK			Financial		40 years
Stop by a branch today			Group
Stop by a branch today			Group

Objectives

1Calculate simple interest.

2Calculate compound interest.

EXAMPLE 2

where the rate r is expressed as an annual (yearly) rate and the time t is expressed in years. This formula can be written more simply without the multiplication raised dots as

I Prt

EXAMPLE 1 If $3,000 is invested for 1 year at a rate of 5%, how much simple interest is earned?

560	Chapter 6 Percent

Simple interest is interest earned only on the original principal. It is found using the following formula.

Simple Interest Formula

Interest principal rate time

I P r t

Self Check 1

If $4,200 is invested for 2 years at a rate of 4%, how much simple interest is earned?

Now Try Problem 17

Strategy We will identify the principal, rate, and time for the investment.

WHY Then we can use the formula I Prt to ﬁnd the unknown amount of simple interest earned.

Solution The principal is $3,000, the interest rate is 5%, and the time is 1 year.


P $3,000	r 5% 0.05		t 1
I Prt		This is the simple interest formula.
I $3,000	0.05 1 Substitute the values for P, r, and t.
I $3,000	0.05	Remember to write the rate r as a decimal.		3,000
		Remember to write the rate r as a decimal.
		Multiply: 0.05 1 0.05.
		Multiply: 0.05 1 0.05.		0.05
I $150		Do the multiplication.		150.00
I $150		Do the multiplication.

The simple interest earned in 1 year is $150.

The information given in this problem and the result can be presented in a table.

Principal	Rate	Time	Interest earned

$3,000	5%	1 year	$150
$3,000	5%	1 year	$150

Self Check 2

If $600 is invested at 2.5% simple interest for 4 years, what will be the total amount of money in the investment account at the end of the 4 years?

If no money is withdrawn from an investment, the investor receives the principal and the interest at the end of the time period. Similarly, a borrower must repay the principal and the interest when taking out a loan. In each case, the total amount of money involved is given by the following formula.

Finding the Total Amount

The total amount in an investment account or the total amount to be repaid on a loan is the sum of the principal and the interest.

Total amount principal interest

If $800 is invested at 4.5% simple interest for 3 years, what will be the total amount of money in the investment account at the end of the 3 years?

Strategy We will ﬁnd the simple interest earned on the investment and add it to the principal.

WHY At the end of 3 years, the total amount of money in the account is the sum of the principal and the interest earned.

Solution The principal is $800, the interest rate is 4.5%, and the time is 3 years. To ﬁnd the interest the investment earns, we use multiplication.

P $800		r 4.5% 0.045	t 3
I Prt		This is the simple interest formula.
I $800	0.045 3 Substitute the values for P, r, and t.
		Remember to write the rate r as a decimal.		4	1
		Remember to write the rate r as a decimal.		4	1
I $36 3		Multiply: $800 0.045 $36.		0.045	36
I $36 3		Multiply: $800 0.045 $36.		800	3
I $108		Do the multiplication.		800	3
I $108		Do the multiplication.		36.000	108

The simple interest earned in 3 years is $108. To ﬁnd the total amount of money in the account, we add.

Total amount principal interest	This is the total amount formula.
$800 $108	Substitute $800 for the principal and
	$108 for the interest.
$908	Do the addition.

At the end of 3 years, the total amount of money in the account will be $908.

Caution! When we use the formula I Prt, the time must be expressed in years. If the time is given in days or months, we rewrite it as a fractional part of a year. For example, a 30-day investment lasts 36530 of a year, since there are 365 days in a year. For a 6-month loan, we express the time as 126 or 12 of a year, since there are 12 months in a year.

EXAMPLE 3	Education Costs A student borrowed $920 at 3% for

9 months to pay some college tuition expenses. Find the simple interest that must be paid on the loan.

Strategy We will rewrite 9 months as a fractional part of a year, and then we will use the formula I Prt to ﬁnd the unknown amount of simple interest to be paid on the loan.

WHY To use the formula I Prt, the time must be expressed in years, or as a fractional part of a year.

Solution Since there are 12 months in a year, we have

			1					9
	9		3	3		3		Simplify the fraction		by removing
9 months	9	year	3	3	year	3	year	Simplify the fraction	12	by removing
								a common factor of 3 from the
	12		3	4		4		a common factor of 3 from the
			1					numerator and denominator.

The time of the loan is 3				year. To ﬁnd the amount of interest, we multiply.
			4
					3				2 1
									2 1
						920			27.60

P $920		r 3% 0.03			t 4
P $920		r 3% 0.03			t 4	0.03			3
I Prt				This is the simple interest formula.		27.60			82.80
I $920 0.03			3	Substitute the values for P, r, and t.				20.70
				Substitute the values for P, r, and t.		4 82.80
			4	Remember to write the rate r as a decimal.		4 82.80
			4	Remember to write the rate r as a decimal.		8
I	$920	0.03	3	Write $920 and 0.03 as fractions.			02
						0
	1	1	4			0
	$82.80								2 8
I	$82.80			Multiply the numerators.		2 8
				Multiply the numerators.					00
	4			Multiply the denominators.

									0
I $20.70				Do the division.					0
									00
									00

The simple interest to be paid on the loan is $20.70.

6.5 Interest

561

Now Try Problem 21

Self Check 3

SHORT-TERM LOANS Find the simple interest on a loan of $810 at 9% for 8 months.

Now Try Problem 25

Short-term Business Loans

EXAMPLE 4

562	Chapter 6 Percent

Self Check 4

ACCOUNTING To cover payroll expenses, a small business owner borrowed $3,200 at a simple interest rate of 15%. Find the total amount he must repay at the end of 120 days.

Now Try Problem 29

To start a business, a couple borrowed $5,500 for 90 days to purchase equipment and supplies. If the loan has a 14% simple interest rate, ﬁnd the total amount they must repay at the end of the 90-day period.

Strategy We will rewrite 90 days as a fractional part of a year, and then we will use the formula I Prt to ﬁnd the unknown amount of simple interest to be paid on the loan.

WHY To use the formula I Prt, the time must be expressed in years, or as a fractional part of a year.

Solution Since there are 365 days in a year, we have

			1						Simplify the fraction	90	by
			1						Simplify the fraction		by
90			5		18	18			365
90			5		18	18			removing a common factor of 5
90 days		year				year		year	removing a common factor of 5
90 days	365	year		5	73	year	73	year	from the numerator and
			1						denominator.
									denominator.

The time of the loan is 1873 year. To ﬁnd the amount of interest, we multiply.

P $5,500 r 14% 0.14 t	90	18
	365	73

I Prt
I $5,500 0.14			18
I $5,500 0.14			73
			73
I	$5,500	0.14		18
I	1	1	73
	1	1	73
I	$13,860
I	73
	73

I $189.86

This is the simple interest formula.

Substitute the values for P, r, and t.

Write $5,500 and 0.14 as fractions.

Multiply the numerators. Multiply the denominators.

Do the division. Round to the nearest cent.

5,500 7700.14 18 22000 6160 55000 7700

770.0013,860

The interest on the loan is $189.86. To ﬁnd how much they must pay back, we add.

Total amount principal interest	This is the total amount formula.
$5,500 $189.86	Substitute $5,500 for the principal and
	$189.86 for the interest.
$5,689.86	Do the addition.
$5,689.86	Do the addition.

The couple must pay back $5,689.86 at the end of 90 days.

2 Calculate compound interest.

Most savings accounts and investments pay compound interest rather than simple interest. We have seen that simple interest is paid only on the original principal. Compound interest is paid on the principal and previously earned interest. To illustrate this concept, suppose that $2,000 is deposited in a savings account at a rate of 5% for 1 year. We can use the formula I Prt to calculate the interest earned at the end of 1 year.

I Prt	This is the simple interest formula.
I $2,000 0.05 1	Substitute for P, r, and t.
I $100	Do the multiplication.

Interest of $100 was earned. At the end of the ﬁrst year, the account contains the interest ($100) plus the original principal ($2,000), for a balance of $2,100.

Suppose that the money remains in the savings account for another year at the same interest rate. For the second year, interest will be paid on a principal of $2,100.

Add the original principal and the interest that it earned to ﬁnd the second-quarter principal.

Compound Interest

EXAMPLE 5

That is, during the second year, we earn interest on the interest as well as on the original $2,000 principal. Using I Prt, we can ﬁnd the interest earned in the second year.

I Prt	This is the simple interest formula.
I $2,100 0.05 1	Substitute for P, r, and t.
I $105	Do the multiplication.

In the second year, $105 of interest is earned. The account now contains that interest plus the $2,100 principal, for a total of $2,205.

As the ﬁgure below shows, we calculated the simple interest two times to ﬁnd the compound interest.

	After 1 year,				After another year,
	calculate the		simple		calculate the	simple
		interest:			interest:
	$100 earned				$105 earned
$2,000				$2,100		$2,205
Original principal				New principal		New principal

If we compute only the simple interest on $2,000, at 5% for 2 years, the interest earned is I $2,000 0.05 2 $200. Thus, the account balance would be $2,200. Comparing the balances, we ﬁnd that the account earning compound interest will contain $5 more than the account earning simple interest.

In the previous example, the interest was calculated at the end of each year, or annually. When compounding, we can compute the interest in other time spans, such as semiannually (twice a year), quarterly (four times a year), or even daily.

As a special gift for her newborn granddaughter, a grandmother opens a $1,000 savings account in the baby’s name. The interest rate is 4.2%, compounded quarterly. Find the amount of money the child will have in the bank on her ﬁrst birthday.

Strategy We will use the simple interest formula I Prt four times in a series of

steps to ﬁnd the amount of money in the account after 1 year. Each time, the time t is 14 .

WHY The interest is compounded quarterly.

Solution If the interest is compounded quarterly, the interest will be computed four times in one year. To ﬁnd the amount of interest $1,000 will earn in the ﬁrst quarter of the year, we use the simple interest formula, where t is 14 of a year.

Interest earned in the ﬁrst quarter:

P1st Qtr $1,000			r 4.2% 0.042		t	1
P1st Qtr $1,000			r 4.2% 0.042		t	4
I Prt				This is the simple interest formula.
I $1,000 0.042			1	Substitute for P, r, and t.
I $1,000 0.042			4				10.5
			4				10.5
I $42		1		Multiply: $1,000 0.042 $42.			4	42.0
							4
		4					4
	$42						02
I	$42			Do the multiplication.			0
							2		0
	4						2		0
	4						2		0
I $10.50				Do the division.			2		0
									0
									0

The interest earned in the ﬁrst quarter is $10.50. This now becomes part of the principal for the second quarter.

P2nd Qtr $1,000 $10.50 $1,010.50

6.5 Interest

563

Self Check 5

COMPOUND INTEREST Suppose $8,000 is deposited in an account that earns 2.3% compounded quarterly. Find the amount of money in an account at the end of the ﬁrst year.

Now Try Problem 33

the interest that it earned to ﬁnd the fourth-quarter principal.

To ﬁnd the interest $1,031.83 will earn in the fourth quarter, we again use the simple interest formula.

Interest earned in the fourth quarter:

Add the third-quarter principal and

the interest that it earned to ﬁnd the third-quarter principal.

To ﬁnd the interest $1,021.11 will earn in the third quarter of the year, we proceed as follows.

Interest earned in the third quarter:

Add the second-quarter principal and

564	Chapter 6 Percent

To ﬁnd the amount of interest $1,010.50 will earn in the second quarter of the year, we use the simple interest formula, where t is again 14 of a year.

Interest earned in the second quarter:

P		$1,010.50	r 0.042		t	1

2nd Qtr					4

I Prt				This is the simple interest formula.
I	$1,010.50 0.042		1	Substitute for P, r, and t.
			4
I	$1,010.50 0.042 1			Multiply.
		4

I $10.61				Use a calculator. Round to the nearest cent (hundredth).

The interest earned in the second quarter is $10.61. This becomes part of the principal for the third quarter.

P3rd Qtr $1,010.50 $10.61 $1,021.11

				1

P3rd Qtr $1,021.11		r 0.042		t
					4
I Prt			This is the simple interest formula.
I $1,021.11 0.042		1	Substitute for P, r, and t.
		4
I	$1,021.11 0.042 1		Multiply.

4
I $10.72			Use a calculator. Round to the nearest cent (hundredth).

The interest earned in the third quarter is $10.72. This now becomes part of the principal for the fourth quarter.

P4th Qtr $1,021.11 $10.72 $1,031.83

						1
P		$1,031.83	r 0.042		t

4th Qtr					4

I Prt				This is the simple interest formula.
I	$1,031.83 0.042		1	Substitute for P, r, and t.
			4
I	$1,031.83 0.042 1			Multiply.
		4

I $10.83				Use a calculator. Round to the nearest cent (hundredth).

The interest earned in the fourth quarter is $10.83. Adding this to the existing principal, we get

Total amount $1,031.83 $10.83 $1,042.66 Add the fourth-quarter principal and the interest that it earned.

The total amount in the account after four quarters, or 1 year, is $1,042.66.

Compounding Daily

EXAMPLE 6

6.5 Interest

565

Calculating compound interest by hand can take a long time. The compound interest formula can be used to ﬁnd the total amount of money that an account will contain at the end of the term quickly.

Compound Interest Formula

The total amount A in an account can be found using the formula

A Pa1 nr bnt

where P is the principal, r is the annual interest rate expressed as a decimal, t is the length of time in years, and n is the number of compoundings in one year.

A calculator is very helpful in performing the operations on the right side of the compound interest formula.

Using Your CALCULATOR Compound Interest

A businessperson invests $9,250 at 7.6% interest, to be compounded monthly. To ﬁnd what the investment will be worth in 3 years, we use the compound interest formula with the following values.

P $9,250 r 7.6% 0.076 t 3 years n 12 times a year (monthly)

A Pa1	r		nt			This is the compound interest formula.
		b
	n	b
				0.076		12(3)
A 9,250a1					b	Substitute the values of P, r, t, and n.
A 9,250a1				12	b	In the exponent, nt means n t.
A 9,250a1				0.076		36
					b	Evaluate the exponent: 12(3) 36.
				12	b	Evaluate the exponent: 12(3) 36.

To evaluate the expression on the right-hand side of the equation using a calculator, we enter these numbers and press these keys.

9250	(	1	.076	12		)		yx	36	11610.43875
							key is used in place of the					key. Also,
On some calculator models, the					^		key is used in place of the				yx	key. Also,
the ENTER	key is pressed instead of the key for the result to be
displayed.

Rounded to the nearest cent, the amount in the account after 3 years will be $11,610.44.

If your calculator does not have parenthesis keys, calculate the sum within the parentheses ﬁrst. Then ﬁnd the power. Finally, multiply by 9,250.

An investor deposited $50,000 in a long-term account at 6.8% interest, compounded daily. How much money will he be able to withdraw in 7 years if the principal is to remain in the bank?

Strategy We will use the compound interest formula to ﬁnd the total amount in the account after 7 years. Then we will subtract the original principal from that result.

Self Check 6

COMPOUNDING DAILY Find the amount of interest $25,000 will earn in 10 years if it is deposited in an account at 5.99% interest, compounded daily.

Now Try Problem 37

WHY When the investor withdraws money, he does not want to touch the original $50,000 principal in the account.

566	Chapter 6 Percent

Solution “Compounded daily” means that compounding will be done 365 times in a year for 7 years.

P $50,000 r 6.8% 0.068 t 7 n 365


A P a1	r		nt
		b
	n	b
A 50,000a1				0.068	b	365(7)

				365
A 50,000a1				0.068	b	2,555
A 50,000a1				365	b
A 80,477.58

This is the compound interest formula.

Substitute the values of P, r, t, and n.		4 3
Substitute the values of P, r, t, and n.		365
In the exponent, nt means n t.		7
		2,555
Evaluate the exponent: 365 7 2,555.
Use a calculator. Round to the nearest cent.

The account will contain $80,477.58 at the end of 7 years. To ﬁnd how much money the man can withdraw, we must subtract the original principal of $50,000 from the total amount in the account.

80,477.58 50,000 30,477.58

The man can withdraw $30,477.58 without having to touch the $50,000 principal.

ANSWERS TO SELF CHECKS

1. $336 2. $660 3. $48.60 4. $3,357.81 5. $8,185.59 6. $20,505.20

S E C T I O N 6.5 STUDY SET

VOCABULARY

Fill in the blanks.

1. In general, is money that is paid for the use of money.

2.In banking, the original amount of money invested, deposited, loaned, or borrowed is known as the

3.The percent that is used to calculate the amount of

interest to be paid is called the interest

4. interest is interest earned only on the original principal.

5. The amount in an investment account is the

sum of the principal and the interest.

6. interest is interest paid on the principal and previously earned interest.

CONCEPTS

7. Refer to the home loan advertisement below.

Loans.com

Great mortgage rates

				30-year
	Home Loan 5%			30-year
	Home Loan 5%			fixed

$125,000 available on-line

a.What is the principal?

b.What is the interest rate?

c.What is the time?

8.Refer to the investment advertisement below.

My Bank

Certificate of Deposit

1
.55% FDIC insured
	Guaranteed returns

•12 month CD

•$10,000 minimum balance

a.What is the principal?

b.What is the interest rate?

c.What is the time?

9.When making calculations involving percents, they must be written as decimals or fractions. Change each percent to a decimal.

a. 7%	b. 9.8%	c. 6	1%
			4

10.Express each of the following as a fraction of a year. Simplify the fraction.

a.	6 months	b.	90 days
c.	120 days	d.	1 month


11.	Complete the table by ﬁnding the simple interest
	earned.

	Principal		Rate	Time		Interest earned

	$10,000		6%	3 years

12.	Determine how many times a year the interest on a
	savings account is calculated if the interest is
	compounded
	a.	annually		b.	semiannually
	c.	quarterly		d.	daily

e.monthly

13.a. What concept studied in this section is illustrated by the diagram below?

b.What was the original principal?

c.How many times was the interest found?

d.How much interest was earned on the ﬁrst compounding?

e.For how long was the money invested?

1st qtr	2nd qtr	3rd qtr		4th qtr

$1,000 $1,050 $1,102.50 $1,157.63 $1,215.51

14.$3,000 is deposited in a savings account that earns 10% interest compounded annually. Complete the series of calculations in the illustration below to ﬁnd how much money will be in the account at the end of 2 years.

Original principal $3,000

First year’s interest

New principal

Second year’s interest

Ending balance

NOTATION

15.Write the simple interest formula I P r t without the multiplication raised dots.

16. In the formula A Pa1 nr b , how many operations must be performed to ﬁnd A?

GUIDED PRACTICE

Calculate the simple interest earned. See Example 1.

17. If $2,000 is invested for 1 year at a rate of 5%, how much simple interest is earned?

6.5 Interest

567

18.If $6,000 is invested for 1 year at a rate of 7%, how much simple interest is earned?

19.If $700 is invested for 4 years at a rate of 9%, how much simple interest is earned?

20.If $800 is invested for 5 years at a rate of 8%, how much simple interest is earned?

Calculate the total amount in each account. See Example 2.

21.If $500 is invested at 2.5% simple interest for

2 years, what will be the total amount of money in the investment account at the end of the

2 years?

22.If $400 is invested at 6.5% simple interest for

6 years, what will be the total amount of money in the investment account at the end of the

6 years?

23.If $1,500 is invested at 1.2% simple interest for 5 years, what will be the total amount of money in the investment account at the end of the

5 years?

24.If $2,500 is invested at 4.5% simple interest for 8 years, what will be the total amount of money in the investment account at the end of the

8 years?

Calculate the simple interest. See Example 3.

25.Find the simple interest on a loan of $550 borrowed at 4% for 9 months.

26.Find the simple interest on a loan of $460 borrowed at 9% for 9 months.

27.Find the simple interest on a loan of $1,320 borrowed at 7% for 4 months.

28.Find the simple interest on a loan of $1,250 borrowed at 10% for 3 months.

Calculate the total amount that must be repaid at the end of each short-term loan. See Example 4.

29.	$12,600 is loaned at a
	simple interest rate of 18%
	for 90 days. Find the total
	amount that must be repaid	Davidian
	at the end of the 90-day	Davidian
	amount that must be repaid	iStockphoto.com/Winston©
	period.
30.	$45,000 is loaned at a
	simple interest rate of 12%
	for 90 days. Find the total
	at the end of the 90-day period.
31.	$40,000 is loaned at 10% simple interest for 45 days.
	Find the total amount that must be repaid at the end
	of the 45-day period.
32.	$30,000 is loaned at 20% simple interest for 60 days.
	Find the total amount that must be repaid at the end
	of the 60-day period.

568	Chapter 6 Percent

Calculate the total amount in each account. See Example 5.

33.Suppose $2,000 is deposited in a savings account that pays 3% interest, compounded quarterly. How much money will be in the account in one year?

34.Suppose $3,000 is deposited in a savings account that pays 2% interest, compounded quarterly. How much money will be in the account in one year?

35.If $5,400 earns 4% interest, compounded quarterly, how much money will be in the account at the end of one year?

36.If $10,500 earns 8% interest, compounded quarterly, how much money will be in the account at the end of one year?

Use a calculator to solve the following problems. See Example 6.

37.A deposit of $30,000 is placed in a savings account that pays 4.8% interest, compounded daily. How much money can be withdrawn at the end of 6 years if the principal is to remain in the bank?

38.A deposit of $12,000 is placed in a savings account that pays 5.6% interest, compounded daily. How much money can be withdrawn at the end of 8 years if the principal is to remain in the bank?

39.If 8.55% interest, compounded daily, is paid on a deposit of $55,250, how much money will be in the account at the end of 4 years?

40.If 4.09% interest, compounded daily, is paid on a deposit of $39,500, how much money will be in the account at the end of 9 years?

APPLICATIONS

41.RETIREMENT INCOME A retiree invests $5,000 in a savings plan that pays a simple interest rate of 6%. What will the account balance be at the end of the ﬁrst year?

42.INVESTMENTS A developer promised a return of 8% simple interest on an investment of $15,000 in her company. How much could an investor expect to make in the ﬁrst year?

43.A member of a credit union was loaned $1,200 to pay for car repairs . The loan was made for 3 years at a simple interest rate of 5.5%. Find the interest due on the loan.

from Campus to Careers

Loan Ofﬁcer

Ariel Skelley/Getty Images

44.REMODELING A homeowner borrows $8,000 to pay for a kitchen remodeling project. The terms of the loan are 9.2% simple interest and repayment in 2 years. How much interest will be paid on the loan?

45.SMOKE DAMAGE The owner of a café borrowed $4,500 for 2 years at 12% simple interest to pay for the cleanup after a kitchen ﬁre. Find the total amount due on the loan.

46.ALTERNATIVE FUELS To ﬁnance the purchase of a ﬂeet of natural-gas–powered vehicles, a city borrowed $200,000 for 4 years at a simple interest rate of 3.5%. Find the total amount due on the loan.

47.SHORT-TERM LOANS A loan of $1,500 at 12.5% simple interest is paid off in 3 months. What is the interest charged?

48.FARM LOANS An apple orchard owner borrowed $7,000 from a farmer’s co-op bank. The money was loaned at 8.8% simple interest for 18 months. How much money did the co-op charge him for the use of the money?

49.MEETING PAYROLLS In order to meet end-of-the- month payroll obligations, a small business had to borrow $4,200 for 30 days. How much did the business have to repay if the simple interest rate was 18%?

50.CAR LOANS To purchase a car, a man takes out a loan for $2,000 for 120 days. If the simple interest rate is 9% per year, how much interest will he have to pay at the end of the 120-day loan period?

51.SAVINGS ACCOUNTS Find the interest earned on $10,000 at 7 14% for 2 years. Use the table to organize your work.

52.TUITION A student borrows $300 from an

educational fund to pay for books for spring semester. If the loan is for 45 days at 3 12% annual interest, what will the student owe at the end of the

loan period?

53.LOAN APPLICATIONS Complete the following loan application.

	Loan Application Worksheet
1.	Amount of loan (principal)		$1,200.00
2.			2 YEARS
	Length of loan (time) __________________
3.			8%
	Annual percentage rate ________________
	(simple interest)
4.	Interest charged ______________________
5.	Total amount to be repaid ______________
6.	Check method of repayment:
	1 lump sum	monthly payments

Borrower agrees to pay ______ equal payments of __________ to repay loan.

54.LOAN APPLICATIONS Complete the following loan application.

	Loan Application Worksheet
1.	Amount of loan (principal)		$810.00
2.			9 mos.
	Length of loan (time) __________________
3.			12%
	Annual percentage rate ________________
	(simple interest)
4.	Interest charged ______________________
5.	Total amount to be repaid ______________
6.	Check method of repayment:
	1 lump sum	monthly payments

Borrower agrees to pay ______ equal payments of __________ to repay loan.

55.LOW-INTEREST LOANS An underdeveloped country receives a low-interest loan from a bank to ﬁnance the construction of a water treatment

plant. What must the country pay back at the end of 3 12 years if the loan is for $18 million at 2.3% simple interest?

56.REDEVELOPMENT A city is awarded a lowinterest loan to help renovate the downtown business

district. The $40-million loan, at 1.75% simple interest, must be repaid in 2 12 years. How much interest will the city have to pay?

A calculator will be helpful in solving the following problems.

57.COMPOUNDING ANNUALLY If $600 is invested in an account that earns 8%, compounded annually, what will the account balance be after 3 years?

58.COMPOUNDING SEMIANNUALLY If $600 is invested in an account that earns annual interest of 8%, compounded semiannually, what will the account balance be at the end of 3 years?

59.COLLEGE FUNDS A ninth-grade student opens a savings account that locks her money in for 4 years at an annual rate of 6%, compounded daily. If the initial deposit is $1,000, how much money will be in the account when she begins college in 4 years?

60.CERTIFICATE OF DEPOSITS A 3-year certiﬁcate of deposit pays an annual rate of 5%, compounded daily. The maximum allowable deposit is $90,000. What is the most interest a depositor can earn from the CD?

61.TAX REFUNDS A couple deposits an income tax refund check of $545 in an account paying an annual rate of 4.6%, compounded daily. What will the size of the account be at the end of 1 year?

									6.5		Interest					569
62.		INHERITANCES After receiving an inheritance of
		$11,000, a man deposits the money in an account
		paying an annual rate of 7.2%, compounded daily.
		How much money will be in the account at the end of
		1 year?
63.		LOTTERIES Suppose you won $500,000 in the
		lottery and deposited the money in a savings account
		that paid an annual rate of 6% interest, compounded
		daily. How much interest would you earn each year?
64.		CASH GIFTS After														Seymour,RichardCopyrightImage fromlicenseunderUsed2009. Shutterstock.com
		receiving a $250,000
		receiving a $250,000
		cash gift, a university
		decides to deposit the
		money in an account
		paying an annual rate
		of 5.88%, compounded
		quarterly. How much
		money will the account contain in 5 years?
65.		WITHDRAWING ONLY INTEREST A ﬁnancial
		advisor invested $90,000 in a long-term account at
		5.1% interest, compounded daily. How much money
		will she be able to withdraw in 20 years if the
		principal is to remain in the account?
66.		LIVING ON THE INTEREST A couple sold their
		home and invested the proﬁt of $490,000 in an
		account at 6.3% interest, compounded daily. How
		much money will they be able to withdraw in 2 years
		if they don’t want to touch the principal?
	WRITING
	WRITING
67.		What is the difference between simple and compound
		interest?
68.		Explain this statement: Interest is the amount of
		money paid for the use of money.
69.		On some accounts, banks charge a penalty if the
		depositor withdraws the money before the end of the
		term. Why would a bank do this?
70.		Explain why it is better for a depositor to open a
		savings account that pays 5% interest, compounded
		daily, than one that pays 5% interest, compounded
		monthly.
	REVIEW
	REVIEW
															2
		Evaluate: B				1					1				2
71.								72.	Evaluate: a					b
71.						4		72.	Evaluate: a			4		b
73.		Add:	3	2				74.	Subtract:	3					2
73.		Add:		5				74.	Subtract:						5
		7		5					7						5
				1		1					1
75.		Multiply: 2				3		76.	Divide: 12						5
75.		Multiply: 2			2	3	3	76.	Divide: 12				2		5
77.		Evaluate: 62						78.	Evaluate: (0.2)2 (0.3)2

570	Chapter 6 Percent

STUDY SKILLS CHECKLIST

Percents, Decimals, and Fractions

Before taking the test on Chapter 6, read the following checklist. These skills are sometimes misunderstood by students. Put a checkmark in the box if you can answer “yes” to the statement.

I know that to write a decimal as a percent, the decimal point is moved two places to the right and a % symbol is inserted.

Decimal Percent

0.2323%

0.768 76.8%

1.50150%

0.9 90%

I know that to write a percent as a decimal, the % symbol is dropped and the decimal point is moved two places to the left.

Percent Decimal

44% 0.44

98.7% 0.987

0.5% 0.005

178.3% 1.783

I know that to write a fraction as a percent, a twostep process is used:

Fraction			decimal			percent

		Divide the		Move the decimal
	numerator by			point two places
	the denominator				to the right
			0.75
			4
			4	3.00
3			2 8			75%
						75%
4			20

I know that to ﬁnd the percent increase (or decrease), we ﬁnd what percent the amount of increase (or decrease) is of the original amount.

The number of phone calls increased from 10 to 18 per day.

Original amount

Amount of increase: 18 10 8

C H A P T E R 6

SUMMARY AND REVIEW

S E C T I O N 6.1

Percents, Decimals, and Fractions

DEFINITIONS AND CONCEPTS

EXAMPLES

Percent means parts per one hundred.

In the ﬁgure below, there are 100 equal-sized square regions, and

The word percent can be written using the symbol %.

37 of them are shaded. We say that

, or 37% , of the ﬁgure is

100

shaded.

Numerator

37%

100

Per 100

															Chapter 6 Summary and Review						571


To write a percent as a fraction, drop the % symbol			Write 22% as a fraction.
and write the given number over 100. Then simplify					22
the fraction, if possible.			22%		22								Drop the % symbol and write 22 over 100.
the fraction, if possible.			22%										Drop the % symbol and write 22 over 100.
				100
				1									To simplify the fraction, factor 22 and 100.
				2 11									To simplify the fraction, factor 22 and 100.
				2 11									Then remove the common factor of 2 from the

					2 50
				1									numerator and denominator.
			Thus, 22% 11 .
					50
Percents such as 9.1% and 36.23% can be written			Write 9.1% as a fraction.
as fractions of whole numbers by multiplying the					9.1
numerator and denominator by a power of 10.			9.1%		9.1									Drop the % symbol and write 9.1 over 100.
numerator and denominator by a power of 10.			9.1%		100									Drop the % symbol and write 9.1 over 100.
					100									To obtain an equivalent fraction of whole
												10		To obtain an equivalent fraction of whole
					9.1							10		numbers, we need to move the decimal point in
					100							10		the numerator one place to the right. Choose
											1				1010 as the form of 1 to build the fraction.
							91							Multiply the numerators.
					1,000									Multiply the denominators.
			Thus, 9.1%				91					.
			Thus, 9.1%									.
							1,000
Mixed number percents,such as 2 31% and 2365%,can be			Write 2 31% as a fraction.
written as fractions of whole numbers by performing			1		2 31
the indicated division.			1		2 31														1
the indicated division.			2	%											Drop the % symbol and write 2				3	over 100.
			3		100
					2		1		100						The fraction bar indicates division.
					2		3		100						The fraction bar indicates division.
					7						1				Write 2	1	as an improper fraction and then
															Write 2	3	as an improper fraction and then
					3					100					multiply by the reciprocal of 100.
							7								Multiply the numerators.
					300										Multiply the denominators.
			Thus, 2	1%			7				.
			Thus, 2	1%							.
				3	300
When percents that are greater than 100% are written			Write 170% as a fraction.
as fractions, the fractions are greater than 1.						170
			170%			170								Drop the % symbol and write 170 over 100.
			170%		100									Drop the % symbol and write 170 over 100.
							1							To simplify the fraction, factor 170 and 100.
						10 17								To simplify the fraction, factor 170 and 100.
						10 17								Then remove the common factor of 10 from the
					10 10									Then remove the common factor of 10 from the
							1							numerator and denominator.
			Thus, 170% 17 .
							10
When percents that are less than 1% are written as			Write 0.03% as a fraction.
fractions, the fractions are less than	1	.
fractions, the fractions are less than		.			0.03
100					0.03
			0.03%												Drop the % symbol and write 0.03 over 100.
			0.03%				100								Drop the % symbol and write 0.03 over 100.
					0.03								100		To obtain an equivalent fraction of whole
					0.03								100		numbers, we need to move the decimal
															numbers, we need to move the decimal
				100									100		point in the numerator two places to the
							1											100
															right. Choose			100 as the form of 1 to build
															the fraction.
															Multiply the numerators and multiply the
							3								denominators. Since the numerator and
							3								denominator do not have any common
							10,000								denominator do not have any common
															factors (other than 1), the fraction is in
											3				simpliﬁed form.
			Thus, 0.03%								3		.
			Thus, 0.03%					10,000					.

572		Chapter 6 Percent

To write a percent as a decimal, drop the % symbol and divide the given number by 100 by moving the decimal point 2 places to the left.

Mixed number percents, such as 1 34% and 10 12%, can be written as decimals by writing the fractional part of the mixed number in its equivalent decimal form.

To write a decimal as a percent, multiply the decimal by 100 by moving the decimal point 2 places to the right, and then insert a % symbol.

To write a fraction as a percent,

1.Write the fraction as a decimal by dividing its numerator by its denominator.

2.Multiply the decimal by 100 by moving the decimal point 2 places to the right, and then insert a % symbol.

Fraction				decimal				percent

Sometimes, when we want to write a fraction as a percent, the result of the division is a repeating decimal. In such cases, we can give an exact answer or an approximate answer.

Write each percent as a decimal.

14% 14.0% 0. 14		Write a decimal point and 0 to
		the right of the 4 in 14%.
9.35% 0. 0935	Write a placeholder 0 (shown in blue)
	to the left of the 9.
198% 198.0% 1. 98		Write a decimal point and 0
		to the right of the 8 in 198%.
0.75% 0. 0075

Write 1 34% as a decimal.

There is no decimal point to move in 1 34%. Since 1 34 1 34 and since the decimal equivalent of 34 is 0.75, we can write 1 34% as 1.75%

3			% 1.75% 0. 0175				Write a placeholder 0 (shown in blue)
1							Write a placeholder 0 (shown in blue)
1	4						to the left of the 1.
Write each decimal as a percent.
0.501						3.66		0.002		0.2%
0.501					50 .1%	3.66	366%	0.002	000 .2%	0.2%
3
Write				as a percent.
Write		4		as a percent.

Step 1 Divide the numerator by the denominator.

0.75 Write a decimal point and some 4 3.00 additional zeros to the right of 3.

2 8

2020

0 The remainder is 0.

Step 2 Write the decimal 0.75 as a percent.

3	0.75 75%
4	0.75 75%

Write 3 as a percent.

Step 1 Divide the numerator by the denominator.

0.666

3 2.000

1 8

2018 2

Write a decimal point and some additional zeros to the right of 2.

The repeating pattern is now clear. We can stop the division.

Step 2 Write the decimal 0.6666 . . . as a percent.

0.6666 66.66 . . .%

Exact Answer:							Approximation:
Use 32 to represent 0.666. . . .							Round to the nearest tenth.
	2	66.66 . . . %						2	66.66 . . . %
3		66.66 . . . %					3		66.66 . . . %
3			u				3


					2		66.7%
			66			%
			66	3		%
				3

13. 0.75%

S E C T I O N

REVIEW EXERCISES

Express the amount of each ﬁgure that is shaded as a percent,as a decimal, and as a fraction. Each set of squares represents 100%.

3.In Problem 1, what percent of the ﬁgure is not shaded?

4.THE INTERNET The following sentence appeared on a technology blog: “54 out of the top 100 websites failed Yahoo’s performance test.”

a.What percent of the websites failed the test?

b.What percent of the websites passed the test?

Write each percent as a fraction.

5.	15%	6.	120%	7.	9	1%	8.	0.2%
						4
Write each percent as a decimal.
9.	27%	10.	8%	11.	655%		12.	1	4%
									5

14. 0.23%

Chapter 6 Summary and Review

573

Write each decimal or whole number as a percent.

15.	0.83	16.	1.625	17.	0.051	18.	6
Write each fraction as a percent.
19.	1	20.	4	21.	7	22.	1
19.	2	20.	5	21.	8	22.	16

Write each fraction as a percent. Give the exact answer and an approximation to the nearest tenth of a percent.

23.	1	24.	5	25.	11	26.	15
	3		6		12		9

27.WATER DISTRIBUTION The oceans contain 97.2% of all of the water on Earth. (Source: National Ground Water Association)

a.Write this percent as a decimal.

b.Write this percent as a fraction in simplest form.

28.BILL OF RIGHTS There are 27 amendments to the Constitution of the United States. The ﬁrst ten are known as the Bill of Rights. What percent of the amendments were adopted after the Bill of Rights? (Round to the nearest one percent.)

29.TAXES The city of Grand Prairie, Texas, has a onefourth of one percent sales tax to help fund park improvements.

a.Write this percent as a decimal.

b.Write this percent as a fraction.

30.SOCIAL SECURITY If your retirement age is 66, your Social Security beneﬁts are reduced by 151 if you retire at age 65. Write this fraction as a percent.

Give the exact answer and an approximation to the nearest tenth of a percent. (Source: Social Security Administration)

6.2 Solving Percent Problems Using

Percent Equations and Proportions

DEFINITIONS AND CONCEPTS	EXAMPLES
The key words in a percent sentence can be	Translate the percent sentence to a percent equation.
translated to a percent equation.
• Each is translates to an equal symbol		What number	is	26%	of	180?
• of translates to multiplication that is
shown with a raised dot		x		26%		180 This is the percent equation.
shown with a raised dot
• what number or what percent translates to
an unknown number that is represented
by a variable.

574

Chapter 6

Percent

Percent sentences involve a

comparison of

12.5%

64.

numbers. The relationship between the base

(the standard of comparison, the whole), the

Amount

percent

base

amount (a part of the base), and the percent is:

(part)

(whole)

Amount percent base

Part percent whole

The percent equation method

What number

45%

120?

We can translate percent sentences to percent

equations and solve to ﬁnd the amount.

45%

120

Translate.

Caution! When solving percent

equations,

Now, solve the percent equation.

always write the percent as a decimal (or

fraction) before performing any calculations.

x 0.45 120

Write 45% as a decimal.

x 54

Do the multiplication.

Thus, 54 is 45% of 120.

We can translate percent sentences to percent

what percent

192?

equations and solve to ﬁnd the percent.

192

Translate.

Now, solve the percent equation.

12 x 192

To isolate x on the right side of the equation, divide

x 192

both sides by 192. Then remove the common factor

192

of 192 in the numerator and denominator.

0.0625 x

On the left side, divide 12 by 192.

06.25%

To write 0.0625 as a percent, multiply it by 100 by

moving the decimal point two places to the right,

and then insert a % symbol.

Thus, 12 is 6.25% of 192.

We can translate percent sentences to percent

8.2

what number?

equations and solve to ﬁnd the base.

Caution! Sometimes the calculations to solve a

8.2

33 31%

Translate.

percent problem are made easier if we write the

Now, solve the percent equation.

percent as a fraction instead of a decimal. This is

the

case with

percents that

have

repeating

8.2

x Write the percent as a fraction: 33

decimal equivalents such as 33

3%, 663%, and

16 2%.

To isolate x on the right side of the equation, divide

8.2

both sides by

. Then remove the common factor of

in the numerator and denominator.

8.2

On the left side, the fraction bar indicates division.

8.2

On the left side, write 8.2 as a fraction. Then use the

rule for dividing fractions: Multiply by the reciprocal of

, which is

3 .

24.6 x

Do the multiplication.

Thus, 8.2 is 331% of 24.6.

amount

base

575

We can translate percent sentences to percent proportions and solve to ﬁnd the amount.

To translate a percent sentence to a percent proportion, use the following form:

Amount is to base as percent is to 100: percent

100

Part is to whole as percent is to 100: part percent

whole 100

We can translate percent sentences to percent proportions and solve to ﬁnd the percent.

We can translate percent sentences to percent proportions and solve to ﬁnd the base.

What number

45%

120?

amount

percent

base

This is the proportion

120

100

to solve.

To make the calculations easier, simplify the ratio 10045 .

x		9			1
			Simplify:	45	5 9	9	.

120	20			100	5 20	20
					1

To solve the proportion we use the cross products.

x 20 120 9 Find the cross products and set them equal.

x 20 1,080 To simplify the right side, do the multiplication: 120 9 1,080.

	1		1,080
	x 20		1,080
	20		20
	20		20
	1
	x		54

Thus, 54 is 45% of 120.

To isolate x on the left side, divide both sides of the equation by 20. Then remove the common factor of 20 from the numerator and denominator.

On the right side, divide 1,080 by 20.

what percent

192?

amount

percent

base

This is the proportion

192

100

to solve.

To make the calculations easier, simplify the ratio 19212 .

		1		x
16				100
1 100			16 x
100			16 x
	100			1
				16 x
16				16
				1
6.25			x

			1	1	1
Simplify:	12		2	2	3	1	.
Simplify:	192	2	2 2	2	2 2 3		.
	192	2	2 2	2	2 2 3	16
		1	1		1

Find the cross products and set them equal.

On the left side, do the multiplication: 1 100 100.

To isolate x on the right side, divide both sides of the equation by 16. Then remove the common factor of 16 from the numerator and denominator.

On the left side, divide 100 by 16.

Thus, 12 is 6.25% of 192.

8.2is 33 13% of what number?

amount			percent			base

					1
		33			1
	8.2	33			3		This is the proportion
	8.2				3

	x			100
							to solve.

576	Chapter 6 Percent
		To make the calculations easier, write the mixed number 331 as the
		improper fraction								100 .							3
		improper fraction								100 .
										3
										100

					8.2					3			Write 33	1	as 1003 .
								x		100			Write 33	3	as 1003 .
								x		100
			8.2 100 x									100	To solve the proportion, ﬁnd the cross products
			8.2 100 x								3		and set them equal.
							820 x					100	To simplify the left side, do the multiplication:
							820 x				3		8.2 100 820.
											1
										x		100	To isolate x on the right side, divide both sides
						820					3		To isolate x on the right side, divide both sides
						820					3		of the equation by 1003			. Then remove the
					100					100			common factor of 1003			from the numerator and
													denominator.
					3						3		denominator.
							100				1		On the left side, the fraction bar indicates
		820					100		x				On the left side, the fraction bar indicates
		820			3				x				division.
			820				3		x				On the left side, write 820 as a fraction. Use
			820				3						the rule for dividing fractions: Multiply by the
		1			100								the rule for dividing fractions: Multiply by the
		1			100								reciprocal of 1003 .
				2,460					x				Multiply the numerators.
		100							x				Multiply the denominators.
		100											Multiply the denominators.
					24.6 x								Divide 2,460 by 100 by moving the understood
													decimal point in 2,460 two places to the left.
		Thus, 8.2 is 331% of 24.6.
					3

	A circle graph is a way of presenting data for	FACEBOOK As of April 2009, Facebook Facebook Users Worldwide
	comparison.The pie-shaped pieces of the graph	had approximately									195		million users			195 Million
	show the relative sizes of each category.	worldwide. Use the information in the
	show the relative sizes of each category.	worldwide. Use the information in the
	The 100 tick marks equally spaced around the	circle graph to the right to ﬁnd how many
	The 100 tick marks equally spaced around the	of them were male.
	circle serve as a visual aid when constructing a	of them were male.
	circle serve as a visual aid when constructing a
	circle graph.	The circle graph shows that 46% of the															Male
		195 million users of Facebook were male.														Female	Male
																	46%
																	46%
																54%

						(Source: O’Reilly Radar)
	Method 1: To ﬁnd the unknown amount write and then solve a percent
	equation.
			is		of
		What number	is	46%	of	195 million?

To solve percent application problems, we often		x		46%		195 Translate.
To solve percent application problems, we often
have to rewrite the facts of the problem in Now, solve the percent equation.
percent sentence form before we can translate		x 0.46 195	Write 46% as a decimal: 46% 0.46.
to an equation.		x 0.46 195	Write 46% as a decimal: 46% 0.46.
to an equation.
		x 89.7	Do the multiplication. The answer is in millions.
	In April of 2009, there were approximately 89.7 million male users of
	Facebook worldwide.

Chapter 6 Summary and Review	577

Method 2: To ﬁnd the unknown amount write and then solve a percent proportion.

What number		is	46%	of	195 million?


	amount		percent			base

195



	46			This is the proportion
	100			This is the proportion
				to solve.

	x	23
195		50
x 50		195 23
x 50		4,485
1		4,485
x 50
50		50

1
	x	89.7

		1
Simplify the ratio:	46		2	23	23.
				50
	100	2			50
		1

Find the cross products and set them equal.

On the right side, do the multiplication.

To isolate x on the left side, divide both sides of the equation by 50. Then remove the common factor of 50 from the numerator and denominator.

On the right side, divide 4,485 by 50. The answer is in millions.

In April of 2009, there were approximately 89.7 million male users of Facebook worldwide.

REVIEW EXERCISES

31.a. Identify the amount, the base, and the percent in the statement “15 is 33 13% of 45.”

b.Fill in the blanks to complete the percent equation (formula):

percent or

Part whole

32.When computing with percents, we must change the percent to a decimal or a fraction. Change each percent to a decimal.

a.	13%	b.	7.1%
c.	195%	d.	1%
			4

When computing with percents, we must change the percent to a decimal or a fraction. Change each percent to a fraction.

e.33 13%

f.66 23%

g.16 23%

33.Translate each percent sentence into a percent equation. Do not solve.

a.What number is 32% of 96?

b.64 is what percent of 135?

c.9 is 47.2% of what number?

34.Translate each percent sentence into a percent proportion. Do not solve.

a.What number is 32% of 96?

b.64 is what percent of 135?

c.9 is 47.2% of what number?

Translate to a percent equation or percent proportion and then solve to ﬁnd the unknown number.

35.What number is 40% of 500?

36.16% of what number is 20?

37.1.4 is what percent of 80?

38.6623% of 3,150 is what number?

39.Find 220% of 55.

40.What is 0.05% of 60,000?

Water 70.9%

578	Chapter 6 Percent

41.43.5 is 7 14% of what number?

42.What percent of 0.08 is 4.24?

43.RACING The nitro–methane fuel mixture used to power some experimental cars is 96% nitro and 4% methane. How many gallons of methane are needed to ﬁll a 15-gallon fuel tank?

44.HOME SALES After the ﬁrst day on the market, 51 homes in a new subdivision had already sold. This was 75% of the total number of homes available. How many homes were originally for sale?

45.HURRICANE DAMAGE In a mobile home park, 96 of the 110 trailers were either damaged or destroyed by hurricane winds. What percent is this? (Round to the nearest 1 percent.)

46.TIPPING The cost of dinner for a family of ﬁve at a restaurant was $36.20. Find the amount of the tip if it should be 15% of the cost of dinner.

47.COLLEGE EXPENSES In 2008, Survey.com asked 500 college students and parents of students who needed a loan, where they turned ﬁrst to pay for college costs. The results of the survey are

shown below in the table. Draw a circle graph for the data.

College	57%
Family/Friends	5%
Local bank	18%
Internet	15%
Other	5%

48.EARTH’S SURFACE The surface of Earth is approximately 196,800,000 square miles. Use the information in the circle graph

to determine the number of square miles of Earth’s surface

that are covered with water.

Land 29.1%

S E C T I O N 6.3	Applications of Percent

DEFINITIONS AND CONCEPTS				EXAMPLES
The sales tax on an item is a percent of the				SHOPPING Find the sales tax and total cost of a $50.95 purchase if
purchase price of the item.				the sales tax rate is 8%.
Sales tax sales tax rate purchase price				Sales tax sales tax rate purchase price
					8%			$50.95
Amount =	percent		base		8%			$50.95
Amount =	percent		base	0.08 $50.95			Write 8% as a decimal: 8% 0.08.
Notice that the formula is based on the percent				0.08 $50.95			Write 8% as a decimal: 8% 0.08.
Notice that the formula is based on the percent				$4.076		Do the multiplication.
equation discussed in Section 6.2.				$4.076		Do the multiplication.
equation discussed in Section 6.2.				$4.08		Round the sales tax to the nearest cent
Sales tax dollar amounts are rounded to the				$4.08		Round the sales tax to the nearest cent
Sales tax dollar amounts are rounded to the						(hundredth).
nearest cent (hundredth).						(hundredth).
nearest cent (hundredth).				Thus, the sales tax is $4.08.The total cost is the sum of its purchase price
The total cost of	an item	is the	sum of its
The total cost of	an item	is the	sum of its	and the sales tax.
purchase price and the sales tax on the item.				and the sales tax.
purchase price and the sales tax on the item.
Total cost purchase price sales tax				Total cost purchase price sales tax rate
Total cost purchase price sales tax					$50.95			$4.08
					$50.95			$4.08
				$55.03		Do the addition.

The total cost of the purchase is $55.03.

Sales tax rates are usually expressed as a percent. APPLIANCES The purchase price of a toaster is $82. If the sales tax is $5.33, what is the sales tax rate?

The sales tax of $5.33 is some unknown percent of the purchase price of $82. There are two methods that can be used to solve this problem.

Chapter 6 Summary and Review

579

There are two methods that can be used to ﬁnd

The percent equation method:

the unknown sales tax rate:

• The percent equation method

$5.33

what percent

82?

5.33

82 Translate.

• The percent proportion method

Now, solve the percent equation.

5.33

x 82

To isolate x on the right side of the equation, divide

both sides by 82.

On the right side of the equation, remove the

0.065

x 82

common factor of 82 from the numerator and

denominator. On the left side, divide 5.33 by 82.

0.065 x

006.5% x

Write the decimal 0.065 as a percent.

6.5% x

The sales tax rate is 6.5%.

The percent proportion method:

5.33

what percent

82?

amount

percent

base

5.33

This is the percent

100

proportion to solve.

5.33 100 82 x

To solve the proportion, ﬁnd the cross products

and set them equal.

533 82 x

Do the multiplication on the left side of the

equation.

To isolate x on the right side, divide both sides

533

of the equation by 82. Then remove the common

factor of 82 from the numerator and denominator.

6.5 x

On the left side, divide 533 by 82.

The sales tax rate is 6.5%.

Instead of working for a salary or getting paid

COMMISSIONS A salesperson earns an 11% commission on all

at an hourly rate, many salespeople are paid on

appliances that she sells. If she sells a $450 dishwasher, what is her

commission.

commission?

The amount of commission paid is a percent of

Commission commission rate

sales

the total dollar sales of goods or services.

11%

$450

Commission commission rate sales

0.11 $450

Write 11% as a decimal.

$49.50

Do the multiplication.

The commission earned on the sale of the $450 dishwasher is $49.50.

The commission rate is usually expressed as a

TELEMARKETING A telemarketer made a commission of $600 in

percent.

one week on sales of $4,000. What is his commission rate?

Commission commission rate

sales

$600

$4,000 Let x represent the

unknown commission

rate.

600

x 4,000

We can drop the dollar signs. To isolate x on

the right side of the equation, divide both

4,000

sides by 4,000.

580

Chapter 6

Percent

Remove the common factor of 4,000 from

0.15

x 4,000

the numerator and denominator. On the

4,000

left side, divide 600 by 4,000.

015%

Write the decimal 0.15 as a percent.

The commission rate is 15%.

To ﬁnd percent of increase or decrease:

WATCHING TELEVISION According to the Nielsen Company, the

1. Subtract the smaller number from the larger

average American watched 145 hours of TV a month in 2007. That

increased to 151 hours per month in 2008. Find the percent of increase.

to ﬁnd the amount of increase or decrease.

Round to the nearest one percent.

2. Find what percent the amount of increase or

First, subtract to ﬁnd the amount of increase.

decrease is of the original amount.

There are two methods that can be used to ﬁnd

151 145 6

Subtract the smaller number from the larger number.

the unknown percent of increase (or decrease):

The number of hours watched per month increased by 6.

• The percent equation method

Next, ﬁnd what percent of the original 145 hours the 6 hour increase

• The percent proportion method

represents.

Caution! The percent of increase (or decrease)

The percent equation method:

is a percent of the original number, that is, the

what percent

145?

number before the change occurred.

145

Translate.

Now, solve the percent equation.

6 x 145

To isolate x on the right side, divide both sides of

x 145 the equation by 145. Then remove the common

145

factor of 145 from the numerator and

denominator.

0.041 x

On the left side, divide 6 by 145.

004 .1% x

Write the decimal 0.041 as a percent.

4% x

Round to the nearest one percent.

Between 2007 and 2008, the number of hours of television watched by

the average American each month increased by 4%.

If the percent proportion method is used, solve the following proportion

for x to ﬁnd the percent of increase.

what percent

145?

amount

percent

base

This is the proportion

145

100

to solve.

The amount of discount is a percent of the

TOOL SALES Find the amount of the discount on a tool kit if it is

original price.

normally priced at $89.95, but is currently on sale for 35% off.Then ﬁnd

Amount of

discount

original

the sale price.

Amount of discount discount rate original price

discount

rate

price

amount

= percent

base

35%

$89.95

0.35 $89.95

Write 35% as a decimal.

Notice that the formula is based on the percent

$31.4825

Do the multiplication.

equation discussed in Section 6.2.

$31.48

Round to the neaerst cent

(hundredth).

			Chapter 6	Summary and Review	581


To ﬁnd the sale price of an item, subtract the	The discount on the tool kit is $31.48. To ﬁnd the sale price, we use
discount from the original price.	subtraction.
Sale price original price discount	Sale price original price discount
		$89.95	$31.48
	$58.47			Do the subtraction.

The sale price of the tool kit is $58.47.

The difference between the original price and

FURNITURE SALES Find the discount rate on a living room set

the sale price is the amount of discount.

regularly priced at $2,500 that is on sale for $1,870. Round to the

Amount of

original

sale

nearest one percent.

We will think of this as a percent-of-decrease problem. The discount

discount

price

(decrease in price) is found using subtraction.

$2,500 $1,870 $630

Discount original price sale price

The living room set is discounted $630. Now we ﬁnd what percent of

the original price the $630 discount represents.

Amount of discount discount rate original price

$630

$2,500

630

x 2,500

Drop the dollar signs. To isolate x

on the right side of the equation,

2,500

divide both sides by 2,500.

On the right side of the equation,

remove the common factor of

0.252

x 2,500

2,500 from the numerator and

2,500

denominator. On the left side,

divide 630 by 2,500.

025 .2% x

Write the decimal 0.252 as a percent.

25% x Round to the nearest one percent.

To the nearest one percent, the discount rate on the living room set is

25%.

REVIEW EXERCISES

49.SALES RECEIPTS Complete the sales receipt shown below by ﬁnding the sales tax and total cost of the camera.

35mm Canon Camera	$59.99
SUBTOTAL	$59.99
SALES TAX @ 5.5%	?
TOTAL	?

50.SALES TAX RATES Find the sales tax rate if the sales tax is $492 on the purchase of an automobile priced at $12,300.

51.COMMISSIONS If the commission rate is 6%, ﬁnd the commission earned by an appliance salesperson who sells a washing machine for $369.97 and a dryer for $299.97.

52.SELLING MEDICAL SUPPLIES A salesperson made a commission of $646 on a $15,200 order of antibiotics. What is her commission rate?

53.T-SHIRT SALES A stadium owner earns a commission of 33 13% of the T-shirt sales from any concert or sporting event. How much can the owner

make if 12,000 T-shirts are sold for $25 each at a soccer match?

54.Fill in the blank: The percent of increase (or

decrease) is a percent of the number, that

is, the number before the change occurred.

582	Chapter 6 Percent

55.THE UNITED NATIONS In 2008, the U.N. Security Council voted to increase the size of a peacekeeping force from 17,000 to 20,000 troops. Find the percent of increase in the number of troops. Round to the nearest one percent. (Source: Reuters)

56.GAS MILEAGE A woman found that the gas mileage fell from 18.8 to 17.0 miles per gallon when she experimented with a new brand of gasoline in her truck. Find the percent of decrease in her mileage. Round to the nearest tenth of one percent.

57.Fill in the blanks.

a.Sales tax sales tax rate

b.Total cost purchase price

c.Commission sales

58.Fill in the blanks.

a.Amount of discount original price

b. Amount of discount

discount rate

c. Sale price original price

59.TOOL CHESTS Use the information in the advertisement below to ﬁnd the discount, the original price, and the discount rate on the tool chest.

Sale price		Save
$2,320	$180!
$2,320
Tool Chest


Professional
quality
quality
7 drawers

60.RENTS Find the discount rate if the monthly rent for an apartment is reduced from $980 to $931 per month.

S E C T I O N 6.4	Estimation with Percent


DEFINITIONS AND CONCEPTS		EXAMPLES
Estimation can be used to ﬁnd approximations		What is 1% of 291.4? Find the exact answer and an estimate using
when exact answers aren’t necessary.		front-end rounding.
To ﬁnd 1% of a number, move the decimal point		Exact answer:
in the number two places to the left.		1% of 291 .4 2.914		Move the decimal point two places to the left.
		1% of 291 .4 2.914		Move the decimal point two places to the left.
		Estimate: 291.4 front-end rounds to 300. If we move the understood
		decimal point in 300 two places to the left, we get 3. Thus
		1% of 291.4 3	Because 1% of 300 3.
To ﬁnd 10% of a number, move the decimal		What is 10% of 40,735 pounds? Find the exact answer and an estimate
point in the number one place to the left.		using front-end rounding.
		Exact answer:
		10% of 40,735 4,073.5			Move the decimal point one place to the left.
		Estimate: 40,735 front-end rounds to 40,000. If we move the understood
		decimal point in 40,000 one place to the left, we get 4,000. Thus
		1% of 40,735 4,000			Because 10% of 40,000 4,000.
To ﬁnd 20% of a number, ﬁnd 10% of the		Estimate the answer:	What is 20% of 809?
number by moving the decimal point one place		Since 10% of 809 is 80.9 (or about 81), it follows that 20% of 809 is
to the left, and then double (multiply by 2) the
to the left, and then double (multiply by 2) the		about 2 81, which is 162. Thus,
result. A similar approach can be used to ﬁnd		about 2 81, which is 162. Thus,
result. A similar approach can be used to ﬁnd		20% of 809 162	Because 10% of 809 81.
30% of a number, 40% of a number, and so on.		20% of 809 162	Because 10% of 809 81.

				Chapter 6 Summary and Review			583


To ﬁnd 50% of a number, divide the number	Estimate the answer:			What is 50% of 1,442,957?
by 2.	We use 1,400,000 as an approximation of 1,442,957 because it is even,

	divisible by 2, and ends with many zeros.
		50% of 1,442,957 700,000 Because 50% of 1,400,000
				1,400,000 700,000.
				2
To ﬁnd 25% of a number, divide the number	Estimate the answer:			What is 25% of 21.004?
by 4.	We use 20 as an approximation because it is close to 21.004 and

	because it is divisible by 4.
		25% of 21.004 5 Because 25% of 20			20	5.
					4
To ﬁnd 5% of a number, ﬁnd 10% of the number	Estimate the answer:			What is 5% of 36,150?
by moving the decimal point in the number one	First, we ﬁnd 10% of 36,150:
place to the left. Then, divide that result by 2.	First, we ﬁnd 10% of 36,150:
place to the left. Then, divide that result by 2.		10% of 36,150 3,615
		10% of 36,150 3,615

	We use 3,600 as an approximation of this result because it is close to
	3,615 and because it is even, and therefore divisible by 2. Next, we
	divide the approximation by 2 to estimate 5% of 36,150.
		3,600	1,800
	2		1,800
	2
	Thus, 5% of 36,150 1,800.
To ﬁnd 15% of a number, ﬁnd the sum of 10% of	TIPPING Estimate the 15% tip on a dinner costing $88.55.
the number and 5% of the number.	To simplify the calculations, we will estimate the cost of the $88.55

	dinner to be $90. Then, to estimate the tip, we ﬁnd 10% of $90 and 5%
	of $90, and add.
		10% of $90 is $9				$9
		5% of $90 (half as much as 10% of $90)				$4.50
	The tip should be $13.50.					$13.50
	The tip should be $13.50.
To ﬁnd 200% of a number, multiply the number	Estimate the answer:			What is 200% of 3.509?
by 2. A similar approach can be used to ﬁnd	To estimate 200% of 3.509, we will ﬁnd 200% of 4. We use 4 as an
300% of a number, 400% of a number, and so on.
300% of a number, 400% of a number, and so on.	approximation because it is close to 3.509 and it makes the
	approximation because it is close to 3.509 and it makes the
	multiplication by 2 easy.
		200% of 3.509 8		Because 200% of 4 2 4 8.
Sometimes we must approximate the percent, to	QUALITY CONTROL In a production run of 145,350 ceramic tiles,
estimate an answer.	3% were found to be defective. Estimate the number of defective
	tiles.
	To estimate 3% of 145,350, we will ﬁnd 1% of 150,000, and multiply
	the result by 3.We use 150,000 as the approximation because it is close
	to 145,350 and it ends with several zeros.
		3% of 145,350 4,500 Because 1% of 150,000 1,500 and
				3 1,500 4,500.
	There were about 4,500 defective tiles in the production run.

Do the addition.

584	Chapter 6 Percent

REVIEW EXERCISES

What is 1% of the given number? Find the exact answer and an estimate using front-end rounding.

61.

342.03

62.

8,687

What is 10% of the given number? Find the exact answer and an estimate using front-end rounding.

63. 43.4 seconds

64. 10,900 liters

Estimate each answer. (Answers may vary.)

65. What is 20% of 63?

67. What is 50% of 279,985?

69. What is 25% of 13.02?

71. What is 5% of 7,150?

73. What is 200% of 29.78?

66. What is 20% of 612?

68. What is 50% of 327?

70. What is 25% of 39.9?

72. What is 5% of 19,359?

74. What is 200% of 1.125?

Estimate a 15% tip on each dollar amount. (Answers may vary.)

75. $243.55

76. $46.99

Estimate each answer. (Answers may vary.)

77.SPECIAL OFFERS A home improvement store sells a 50-ﬂuid ounce pail of asphalt driveway sealant that is labeled “25% free.” How many ounces are free?

78.JOB TRAINING 15% of the 785 people attending a job training program had a college degree. How many people is this?

Approximate the percent and then estimate each answer. (Answers may vary.)

79.SEAT BELTS A state trooper survey on an interstate highway found that of the 3,850 cars that passed the inspection point, 6% of the drivers were not wearing a seat belt. Estimate the number not wearing a seat belt.

80.DOWN PAYMENTS Estimate the amount of an 11% down payment on a house that is selling for $279,950.

S E C T I O N 6.5 Interest

DEFINITIONS AND CONCEPTS

Interest is money that is paid for the use of money.

Simple interest is interest earned on the original principal and is found using the formula

I Prt

where P is the principal, r is the annual (yearly) interest rate, and t is the length of time in years.

The total amount in an investment account or the total amount to be repaid on a loan is the sum of the principal and the interest.

Total amount principal interest

EXAMPLES

If $4,000 is invested for 3 years at a rate of 7.2%, how much simple interest is earned?

P $4,000	r 7.2% 0.072	t 3
I Prt	This is the simple interest formula.
I $4,000 0.072 3 Substitute the values for P, r, and t.
	Remember to write the rate r as a decimal.
I $288 3	Multiply: $4,000 0.072 $288.
I $864	Do the multiplication.

The simple interest earned in 3 years is $864.

HOME REPAIRS A homeowner borrowed $5,600 for 2 years at 10% simple interest to pay for a new concrete driveway. Find the total amount due on the loan.


P $5,600	r 10% 0.10		t 2
I Prt		This is the simple interest formula.
I $5,600 0.10 2		Write the rate r as a decimal.
I $560 2		Multiply: $5,600 0.10 $560.
I $1,120		Do the multiplication.

The interest due in 2 years is $1,120. To ﬁnd the total amount of money due on the loan, we add.

Total amount principal interest

$5,600 $1,120

$6,720

At the end of 2 years, the total amount of money due on the loan is $6,720.

Chapter 6

Summary and Review

585

When using the formula I Prt, the time must

FINES A man borrowed $300 at 15% for 45 days to get his car out of

be expressed in years. If the time is given in days

an impound parking garage. Find the simple interest that must be paid

or months, rewrite it as a fractional part of a year.

on the loan.

Here are two examples:

Since there are 365 days in a year, we have

• Since there are 365 days in a year,

45 days

year

5 9

year

Simplify the fraction.

5 12

365

5 73

60 days 365 year 5 73 year

73 year

The time of the loan is

year. To ﬁnd the amount of interest, we

• Since there are 12 months in a year,

multiply.

4 months

year

3 4

year

P $300

r 15% 0.15

I Prt

This is the simple interest formula.

I $300 0.15

Write the rate r as a decimal.

$300

0.15

Write $300 and 0.15 as fractions.

$405

Multiply the numerators.

Multiply the denominators.

I $5.55 Do the division. Round to the nearest cent.

The simple interest that must be paid on the loan is $5.55.

Compound interest is interest earned on the

COMPOUND INTEREST Suppose $10,000 is deposited in an

original principal and previously earned interest.

account that earns 6.5% compounded semiannually. Find the amount

When compounding, we can calculate interest:

of money in an account at the end of the ﬁrst year.

• annually: once a year

The word semiannually means that the interest will be compounded

two times in one year. To ﬁnd the amount of interest $10,000 will earn

• semiannually: twice a year

in the ﬁrst half of the year, use the simple interest formula, where t is

• quarterly: four times a year

1 of a year.

• daily: 365 times a year

Interest earned in the ﬁrst half of the year:

P $10,000

r 6.5% 0.065

I Prt

This is the simple interest formula.

I $10,000 0.065

Write the rate r as a decimal.

$10,000

0.065

Write $10,000 and 0.065 as fractions.

$650

Multiply the numerators.

Multiply the denominators.

I $325

Do the division.

The interest earned in the ﬁrst half of the year is $325. The original

principal and this interest now become the principal for the second

half of the year.

$10,000 $325 $10,325

To ﬁnd the amount of interest $10,325 will earn in the second half of

the year, use the simple interest formula, where t is again 1 of a year.

586

Chapter 6

Percent

Interest earned in the second half of the year:

P $10,325

r 6.5% 0.065

I Prt

This is the simple interest formula.

I $10,325

0.065

Write the rate r as a decimal.

$10,325

0.065

Write $10,325 and 0.065 as fractions.

$671.125

Multiply the numerators.

Multiply the denominators.

I $335.56

Do the division. Round to the nearest cent.

The interest earned in the second half of the year is $335.56. Adding

this to the principal for the second half of the year, we get

$10,325 $335.56 $10,660.56

The total amount in the account after one year is $10,660.56

Computing compound interest by hand can take

COMPOUNDING DAILY A mini-mall developer promises investors

a long time. The compound interest formula can

in his company 3 41% interest, compounded daily. If a businessman

be used to ﬁnd the amount of money that an

decides to invest $80,000 with the developer, how much money will be

account will contain at the end of the term.

in his account in 8 years?

A Pa1

Compounding daily means the compounding will be done 365 times a

year.

where A is the amount in the account, P is the

P $80,000

r 3

% 0.0325

t 8

n 365

principal, r is the annual interest rate, n is the

number of compoundings in one year, and t is

A Pa1

This is the compound interest formula.

the length of time in years.

calculator is

helpful in performing the

0.0325

365(8)

operations on the right side of the compound

A 80,000a1

Substitute for P, r, n, and t.

365

interest formula.

A 80,000a1

0.0325

2,920

365

Evaluate the exponent: 365 8 2,920.

A 103,753.21 Use a calculator. Round to the nearest cent.

There will be $103,753.21 in the account in 8 years.

REVIEW EXERCISES

81.INVESTMENTS Find the simple interest earned on $6,000 invested at 8% for 2 years. Use the following table to organize your work.

82.INVESTMENT ACCOUNTS If $24,000 is invested at a simple interest rate of 4.5% for 3 years, what will be the total amount of money in the investment account at the end of the term?

83.EMERGENCY LOANS A teacher’s credit union loaned a client $2,750 at a simple interest rate of 11% so that he could pay an overdue medical bill. How much interest does the client pay if the loan must be paid back in 3 months?

84.CODE VIOLATIONS A business was ordered to correct safety code violations in a production plant. To pay for the needed corrections, the company borrowed $10,000 at 12.5% simple interest for 90 days. Find the total amount that had to be paid after 90 days.

Chapter 6 Summary and Review

587

85.MONTHLY PAYMENTS A couple borrows $1,500 for 1 year at a simple interest rate of 7 34%.

a.How much interest will they pay on the loan?

b.What is the total amount they must repay on the loan?

c.If the couple decides to repay the loan by making 12 equal monthly payments, how much will each monthly payment be?

86.SAVINGS ACCOUNTS Find the amount of money that will be in a savings account at the end of 1 year if $2,000 is the initial deposit and the interest rate of 7% is compounded semi-annually. (Hint: Find the simple interest twice.)

87.SAVINGS ACCOUNTS Find the amount that will

be in a savings account at the end of 3 years if a deposit of $5,000 earns interest at a rate of 6 12%, compounded daily.

88.CASH GRANTS Each year a cash grant is given to

adeserving college student. The grant consists of the interest earned that year on a $500,000 savings account. What is the cash award for the year if the money is invested at a rate of 8.3%, compounded daily?

16 b. 9

588

C H A P T E R 6 TEST

1.Fill in the blanks.

a.means parts per one hundred.

b.The key words in a percent sentence translate as follows:

•translates to an equal symbol

•translates to multiplication that is shown with a raised dot

•number or percent translates to an unknown number that is represented by a variable.

c.In the percent sentence “5 is 25% of 20,” 5 is the

, 25% is the percent, and 20 is the

d.When we use percent to describe how a quantity has increased compared to its original value, we

are ﬁnding the percent of

e.interest is interest earned only on the

original principal. interest is interest

paid on the principal and previously earned interest.

2.a. Express the amount of the ﬁgure that is shaded as a percent, as a fraction, and as a decimal.

b.What percent of the ﬁgure is not shaded?

3.In the illustration below, each set of 100 square regions represents 100%. Express as a percent the amount of the ﬁgure that is shaded. Then express that percent as a fraction and as a decimal.

4. Write each percent as a decimal.

a. 67%	b. 12.3%	c. 9	3	%
			4

5. Write each percent as a decimal.
a. 0.06%	b. 210%	c. 55.375%

6. Write each fraction as a percent.
1		5			28
a.		b.		c.
	4		8		25

7. Write each decimal as a percent.
a. 0.19	b. 3.47	c. 0.005

8. Write each decimal or whole number as a percent.

a. 0.667 b. 2 c. 0.9

9. Write each percent as a fraction. Simplify, if possible.

a. 55% b. 0.01% c. 125%

10. Write each percent as a fraction. Simplify, if possible.

	2
a. 6	3%	b. 37.5%	c. 8%

11.Write each fraction as a percent. Give the exact answer and an approximation to the nearest tenth of a percent.

1 a. 30

12.65 is what percent of 1,000?

13.What percent of 14 is 35?

14.FUGITIVES As of November 29, 2008, exactly 460 of the 491 fugitives who have appeared on the FBI’s Ten Most Wanted list have been captured or located. What percent is this? Round to the nearest tenth of one percent. (Source: www.fbi.gov/wanted)

WANTED BY THE

FBI

15.SWIMMING WORKOUTS A swimmer was able to complete 18 laps before a shoulder injury forced him to stop. This was only 20% of a typical workout. How many laps does he normally complete during a workout?

16.COLLEGE EMPLOYEES The 700 employees at a community college fall into three major categories, as shown in the circle graph. How many employees are in administration?

Administration

Classified

42%

Certificated

55%

17.What number is 224% of 60?

18.2.6 is 3313% of what number?

Chapter 6 Test

589

19.SHRINKAGE See the following label from a new pair of jeans. The measurements are in

inches. (Inseam is a measure of the length of the jeans.)

a.How much length will be lost due to shrinkage?

b.What will be the length of the jeans after being washed?

WAIST INSEAM

33 34

Expect shrinkage of approximately

in length after the jeans are washed.

20.TOTAL COST Find the total cost of a $25.50 purchase if the sales tax rate is 2.9%.

21.SALES TAX The purchase price for a watch is $90. If the sales tax is $2.70, what is the sales tax rate?

22.POPULATION INCREASES After a new freeway was completed, the population of a city it passed through increased from 2,800 to 3,444 in two years. Find the percent of increase.

23.INSURANCE An automobile insurance salesperson receives a 4% commission on the annual premium of any policy she sells. Find her commission on a policy if the annual premium is $898.

24.TELEMARKETING A telemarketer earned a commission of $528 on $4,800 worth of new business that she obtained over the telephone. Find her rate of commission.

25.COST-OF-LIVING A teacher earning $40,000 just received a cost-of-living increase of 3.6%. What is the teacher’s new salary?

590	Chapter 6 Test

26.AUTO CARE Refer to the advertisement below. Find the discount, the sale price, and the discount rate on the car waxing kit.

SAVE! SAVE! SAVE! SAVE!

CAR WAX KIT

$9 OFF

Regularly $75.00

27.TOWEL SALES Find the amount of the discount on a beach towel if it regularly sells for $20, but is on sale for 33% off. Then ﬁnd the sale price of the towel.

28.Fill in the blanks.


a.	To ﬁnd 1% of a number, move the decimal point
	in the number	places to the		.
b.	To ﬁnd 10% of a number, move the decimal point
	in the number	place to the	.

29.Estimate each answer. (Answers may vary.)

a.What is 20% of 396?

b.What is 50% of 6,189,034?

c.What is 200% of 21.2?

30.BRAKE INSPECTIONS Of the 1,920 trucks inspected at a safety checkpoint, 5% had problems with their brakes. Estimate the number of trucks that had brake problems?

31.TIPPING Estimate the amount of a 15% tip on a lunch costing $28.40.

32.CAR SHOWS 24% of 63,400 people that attended a ﬁve-day car show were female. Estimate the number of females that attended the car show.

33.INTEREST CHARGES Find the simple interest on a loan of $3,000 at 5% per year for 1 year.

34.INVESTMENTS If $23,000 is invested at 412% simple interest for 5 years, what will be the total

amount of money in the investment account at the end of the 5 years?

35.SHORT-TERM LOANS Find the simple interest on a loan of $2,000 borrowed at 8% for 90 days.

36. Use the formula A Pa1 nr b to ﬁnd the amount

of interest earned on an investment of $24,000 paying an annual rate of 6.4% interest, compounded daily for 3 years.

<<< < Предыдущая 34 35 36 37 38 39 40 41 42 43 44 4546 / 6746 47 48 49 50 51 52 53 54 55 56 57 58 > Следующая >>>

Соседние файлы в предмете [НЕСОРТИРОВАННОЕ]

#
10.12.2018408.58 Кб6antikrizisnoe-upravlenie.doc
#
18.12.2018108.03 Кб6ARHITYeKTURA.doc
#
10.06.20158.32 Mб302aswath_damodaran-investment_philosophies_2012.pdf
#
10.06.201582.94 Кб7audit_risk.doc
#
10.06.20154.17 Mб5BallotingApplicationDocs-SIMSUsersGuide.pdf
#
10.06.201515.55 Mб147basic mathematics for college students.pdf
#
10.06.2015901.06 Кб40Bazy_dannykh_i_znanii_UP_SHirokov_L.A._2000.pdf
#
29.03.20162.45 Mб35Bernd_Fon_Vittenburg_-_Shakh_planete_Zemlya.pdf
#
10.06.201561.93 Кб44bezopasnost.docx
#
10.06.20152.89 Mб85bibliofond_ru_604241.docx
#
10.06.20152.1 Mб30blind_watchmaker.pdf