The flat rate trap
Before computers were used regularly, lenders had to rely on hand-calculated figures, and so they often looked for easy short cuts. One such approach is still seen today and can be very misleading for short term loans unless you are wary. It is the use of the so-called flat rate of interest.
Let us say a lender provided a loan of Ј1,000, to be repaid monthly over one year and simply quoted 14% pa as the interest rate, compounding annually. You might be forgiven if you thought the following lender’s explanation of his calculation to seem fair.
14% of Ј1,000 is Ј140. So in one year, the amount lent including interest is Ј1,140. If the loan is repaid in 12 equal monthly instalments, that works out to a twelfth of Ј1,140 each month which is Ј95 per month exactly, since 12 x 95 = 1,140.
This sounds like a straightforward loan @ 14% pa. But the true annual rate in this example is actually 27.96 % pa. which is almost double the quoted rate. This is
because part of the monthly payment is actually repaying capital each month, so the capital debt is not Ј1,000 for the whole year. The facile, flat rate calculation assumed interest was always charged on Ј1,000 as if it was outstanding for the whole year, when on average only about half of it was owed over the period. Thus, the 14% quoted rate is about half the true rate.
The rate of interest of 14% used in this example is a flat rate. The table in Figure 8 illustrates the schedule that amortises the loan if the true monthly interest rate is 2.0757 % or 27.96% pa true rate.
In reality, the interest each month is equal to the monthly rate (2.0757% pm) applied to the debt at the end of the previous month. The debt at the end of each month is equal to the previous month’s debt plus interest for the month, less repayments made in the month. Alternatively, current debt is the previous month’s debt less the capital element repaid – the calculation works out the same either way.