The time value of money

When lending (and borrowing) money, the timing of payments of interest and return of capital has a significant effect on the interest rate. For interest receipts it is called the AER (annual equivalent rate). In the case of interest payments, such as for a mortgage, it is called the APR (annual percentage rate) but is effectively the same thing.

When VAT on fuel was introduced in 1994, many people paid in advance to save the 8% tax. Decisions like this should consider the effective rate of return on the investment for the period.

Assuming your annual fuel bill is £100, what is the effective rate of return?

On the face of it, you might say 8%, because that is what you have saved.

However, taking account of the time value of money, you need to allow for the fact that normally you pay monthly or quarterly. So, ignoring seasonal variations, you would have only paid 7 1/2 months in advance on average.

Consequently the effective AER (annual equivalent rate) of 8% over 7 1/2 months is 13%.

Bearing in mind that it was effectively after tax, this was easily the best investment in 1994.

The effect of compound interest

Compound interest arises where interest is left in an investment and itself then earns interest. For example, doubling your money in such an investment takes:

• ten years at an interest rate of 5%
• seven years at 10%
• only five years at 15%

Another example comes from pensions. To achieve a pension of £10,000 a year from the age of 65, a man needs to contribute:

• starting at age 30, £150 a month
• starting at 40, £300 a month
• starting at 50, £600 a month

(For a woman it is 10% more in each case.)

The effect of inflation

'Real' rates of interest are the rates in excess of inflation. Only these rates preserve the real value of the capital. Usually they are in the region of 3%, whatever the actual rate.

However, since all interest is taxable, high interest rates can result in negative real rates, so they are not necessarily a good thing for taxpayers.

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