7.1The rate of interest

Economists talk about the rate of interest. This assumes that there is some particular

interest rate that can be taken as representative of all interest rates in an economy.

The rate chosen as the representative rate will vary depending on the question being

considered. Sometimes, for example, the discount rate on treasury bills will be taken

as representative. At other times the rate of interest on new local authority debt,

the base interest rate of the retail banks, or a short-term money market rate such as

LIBOR might be used. No matter which rate is chosen, it is implied that the interest

rate structure is stable and that all interest rates in the economy are likely to move

in the same direction. If this is true, we should be able to explain what determines

202

....

FINM_C07.qxd 1/18/07 11:33 AM Page 203

7.1 The rate of interest

interest rates in general. Before going on to look at this question, however, we need

to distinguish between nominal and real interest rates.

The rates of interest quoted by nancial institutions are nominal rates, allowing

calculation of the amounts of money to be received as interest by lenders or paid by

borrowers. This is clearly of immediate interest to borrowers and lenders. However,

it is equally important to them to know how these amounts relate to their existing

or likely future income and to the prices of goods and services. That is, a borrower

wishes to know the opportunity cost of borrowing – how many goods and services

she must forgo in order to pay the interest on a loan.

Consider the position of someone who takes out a £50,000 mortgage on a house

over 25 years at a xed nominal rate of interest of, say, 6 per cent. Assume further

that the annual gross income of the borrower is £20,000. In the rst year of the loan,

interest on the £50,000 debt will amount to £3,000 – 15 per cent of the borrower’s

annual gross income. Assume, however, that the economy is experiencing an annual

rate of ination of 2.5 per cent and that the borrower’s gross annual income rises in

line with ination. That is, the real value of the borrower’s income has not changed

– he is able to buy the same quantity of goods and services as before. However, the

loan repayments remain the same in money terms and make up a smaller and smaller

proportion of the borrower’s income. Thus, the real cost of the interest payments

declines over time. Therefore we can speak of the real rate of interest– the rate of

interest adjusted to take into account the rate of ination.

In this example, the real rate of return to the lender is also falling over time –

the interest received would, in each successive year, buy fewer and fewer goods and

services because of the existence of ination. It follows that lenders attempt to set

interest rates to take into account the expected rate of ination over the period of a

loan. If lenders cannot be condent about the real rate of return they are likely to

receive, they will be willing to lend at xed rates of interest for short periods only.

At the end of the loan period, the borrower might then be able to continue the loan,

requiring it to be ‘rolled over’ at a newly set rate of interest, which can reect any

changes in the expected rate of ination. Alternatively, lenders can set a oating rate

of interest that is automatically adjusted in line with changes in the rate of ination.

Real interest rate:The nominal rate of interest minus the expected rate of ination.

It is a measure of the anticipated opportunity cost of borrowing in terms of goods and

services forgone.

As we have suggested above, it is the expected rate of ination over the period

of a loan that is of particular importance, rather than the present rate of ination.

Consider a simple example. Assume that a bank is willing to make a loan to you of

£1,000 for one year at a real rate of interest of 3 per cent. This means that at the end

of the year the bank expects to receive back £1,030 of purchasing power at current

prices. However, if the bank expects a 10 per cent rate of ination over the next

twelve months, it will want £1,133 back (10 per cent above £1,030). The interest rate

required to produce this sum would be 13.3 per cent.

203

....

FINM_C07.qxd 1/18/07 11:33 AM Page 204

Chapter 7 • Interest rates

This can be formalised as follows:

i(1 r)(1 Ge)
1	(7.1)

where iis the nominal rate of interest, ris the real rate of interest and G^eis the

expected rate of ination (both expressed in decimals). In our example above, we

would have

i(1 0.03)(1 0.1) 1

(1.03)(1.1) 1

1.133 1

0.133 or 13.3 per cent

For most purposes, we can use the simpler, although less accurate, formula

irGe

(7.2)

In our example, this would give us 3 per cent plus 10 per cent = 13 per cent.

Expressedthe other way around eqn 7.2 becomes

riGe

(7.3)

If we next assume that ris stable over time, we arrive at what is widely known

as the Fisher effect, after the American economist Irving Fisher. This suggests that

changes in short-term interest rates occur principally because of changes in the

expected rate of ination. If we go further and assume that expectations held by

market agents about the rate of ination are broadly correct, the principal reason for

changes in interest rates becomes changes in the current rate of ination. We could,

in that case, write:

riG

(7.4)

We are implying here that borrowers and lenders think entirely in real terms.

This leaves us to consider the factors that determine real rates of interest. The

central theoretical explanation of real interest rates is known as the loanable funds

theory.