# Interest Rates

Monthly
Statistical Bulletin Feature Articles

Money is borrowed so that goods and services can be purchased now rather than in the future and interest is the cost involved, or the price paid, for the use of that money.

The amount of interest paid is determined by the amount of money borrowed, the length of time to be taken to pay back the money (plus interest) and the interest rate.

This note will look at what makes an interest rate and also the three interest rates that are published in Chapter 5, viz the prime rate, the housing rate and the unofficial cash rate.

**What makes an interest rate?**

An interest rate is comprised of 3 parts that are necessary to compensate the lender for lending money. These parts are compensation for

- risk - in lending money there is a risk involved that the lender may lose part or all of the original amount (the principal) lent
- inflation - in times of price inflation the principal loses purchasing power and the longer the period of the loan and the higher the rate of inflation the greater the value that would be lost
- waiting - by waiting, the lender is forgoing present spending on goods or services or the ability to invest the cash in other ventures should favourable circumstances arise.

**Real interest rates**

For whatever purpose that money is borrowed there is an interest
rate quoted. This interest rate is known as the *nominal*
rate and it may vary from time period to time period.

Often it is desirable to be able to directly compare the
interest rate for a particular type of loan between time periods
(or to compare interest rates for different types of loans for the
same period). To do this the *real* interest rate is
calculated by removing the rate of inflation from the nominal
rate.

The nominal interest rate can be shown algebraically as:

n = r + i + (i x r)

where

n = nominal interest rate

r = real interest rate

i = inflation rate.

(In the equation all rates are expressed as decimals, eg 5% becomes 0.05.)

Therefore, by rearranging the equation, the real interest rate is:

r = (n - i) / (1 + i)

(In times of low inflation the denominator will be very close to 1 and the real interest rate will be approximately the nominal rate less the inflation rate.)

The real interest rate comprises the compensation required for risk and for waiting.

**Why different interest rates?**

Since inflation affects all lenders to much the same extent and, to a large extent, the compensation for waiting can be assumed to be very similar among lenders, then the difference between the interest rates for different types of loans reflects the risk factor. (This risk factor may also include a margin that provides extra "profit" and/or covers costs involved in providing the loan.)

Lending to government is very low risk and this is reflected in bond rates being at the low end of the range of interest rates quoted in the financial markets. Similarly, lending to banks (ie bank deposits) is also low risk and hence only attracts low interest rates. Housing loans are considered more risky so the interest rates are higher and lending to business is more risky still and hence even higher rates.

This table shows the *prime interest rate* which is the
predominant indicator rate offered by banks for large, variable
rate business loans. These sorts of loans comprise overdrafts and
fully drawn loans.

Both the nominal and real prime rates are tabled and graphed with the real rate calculated using the inflation rate as measured by the Consumer Price Index.

From the table and graph it can be seen that although the nominal rate has been decreasing since August 1996 the real rate has hovered at or above 8% and is higher than at any time since March 1993.

This table shows the unofficial cash rate and the banks' housing loan rate.

The unofficial cash rate, or the cash market 11 a.m. call rate, is the rate paid on unsecured overnight loans of cash. The movements in this rate are directly influenced by the operation of the Reserve Bank in the money market.

The banks' housing loan rate is the predominant rate of the large home lending banks for lending to (mainly) owner-occupiers. Over recent years this rate has followed the unofficial rate, usually with a lag of one month. The difference between the two rates highlights the extra premium for risk that the banks require.

This feature was prepared by Stephen Barber.