My father was recently approached by a salesman who described himself as a “kitchen designer” and tried to persuade us to have our kitchen refitted. In the course of conversation the salesman produced the following calculations to show that it would be much cheaper to accept credit at over 20% from his firm than to take money out of a building society where it was earning interest at 10% (the building society calculation was set out on a year-by-year schedule but the end result was the same).
I cannot see how interest at 23.8% can come to less than interest at 10%, so could you explain where the error is? (Incidentally, my father did not agree to have the kitchen refitted!)
This is a good example of the ways in which salesmen and their financial advisers can set out figures which give a completely misleading impression (and also the reason why a sound understanding of the principles of compound interest is essential for students of valuation).
The problem arises simply because the two sets of figures are not on the same basis, and in fact differ in three respects:
- the building society investment is annual but the finance house loan is monthly;
- building society interest is calculated at the end of 10 years, but the finance loan is calculated to the start of the period;
- the accumulation of building society interest is based on compound interest but the finance house loan does not take this into account.
Each example can be converted to the basis of the other, but before doing so we will simplify the problem by converting the loan offer to an equivalent annual payment. In order to do this we must first calculate the true annual interest rate.
The use of the internal rate of return has been discussed in this column on previous occasions (EG 246: 1028, 247: 149), so we will simply state that we are trying to find the rate of interest at which the discounted payments exactly equal the original cost of £5,000. This turns out to be 1.532% per month or 20.014% per annum, and a check calculation can be set out as follows:
To find the equivalent annual payment, we multiply the loan by the annuity £1 will purchase (ie the reciprocal of the years’ purchase) at the corresponding annual rate of interest:
In other words, if the borrower invested £91.33 each month in some security at 20.014% it would accumulate to £1193.21 at the end of the year and, if he then paid this to the finance company each year, they would both be in the same financial position.
Now let us return to the main problem. We can rework the loan figures to match the building society calculation above as follows:
This is a very different matter from the salesman’s example!
Alternatively we could rework the building society example to match the finance house loan, but note carefully that compound interest is not taken into account in this method. (Remember that the annual sum for the loan is £1,193.21.)
Again the finance house loan at £5,960 is clearly more expensive!
To summarise, the difference between the two calculations given by the salesman is that the building society is based on proper compound interest calculation but the finance house example is based only on simple interest on the calculated monthly repayment, and makes no allowance for interest accumulating on each instalment.
The moral of all this is that everyone concerned with financial calculations should understand the principles thoroughly, be able to advise lay persons on the relative merits of different forms of finance, and not take glossy quotations at their face value.