Step-by-step calculation of loan installments

 By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

21 October 2012

Harriet K. of Mombasa is lucky because she has asked the question that will help us understand the formula for calculating loan repayment installments using the reducing balance method. Her specific situation is that she took a loan of Sh186,665 repayable in three years at 21.4 per cent interest per annum. The bank has told her that she will be paying Sh7,071 per month but she is wondering how they arrived at that figure.

At first sight, the reducing balance formula for calculating the monthly installments for a loan is quite easy: it is the monthly simple interest divided by a time-interest-rate-factor. But the calculation must be done carefully in a three stage process

Stage one is to calculate the monthly simple interest.  This is done in two steps, thus: we start by dividing the annual interest by 12 and then multiply the result by the loan amount. In Harriet’s case, the annual interest rate is 21.4 per cent (=0.214), so, the monthly simple interest rate is 0.017833. Multiplying this by the loan amount (Sh186,665), we get Sh3,329.

Stage two of the process is to calculate the time-interest-rate-factor. Now I must caution that the name “time-interest-rate-factor” is my own creation – so those with Internet access shouldn’t run to Google it! This factor is obtained in four steps as follows.

In the first step, we add the number one to the monthly interest rate. In Harriet’s loan, the monthly interest rate is 0.017833, thus adding one to this yields 1.017833.

The second step is to raise the result from step one to a power equal to the number of months of the loan. Harriet’s loan is payable in 3 years, therefore the power is 36. Thus we need 1.017833 is raised to power 36.

In other words, we need to multiply 1.017833 by itself 36 times! Now doing that with an ordinary calculator can be tedious. Furthermore, there is a high chance that one will make a mistake in counting the number of times that the multiplication has been done. Luckily though, a scientific calculator will do it at the push of a single button. The answer comes to 1.88956.

The third step is easy: we calculate the reciprocal of the result from step two; that is, the number one divided by 1.88956. That answer is 0.52922.

In the fourth step we subtract the result of step three from one; that is, 1 – 0.52922 = 0.47078. This final figure is what I am calling the “time-interest-rate-factor”. You will notice that it is a manipulation of the interest rate and the duration of the loan – hence the name. We are now ready to evaluate the monthly instalment.

Remember, it is the monthly simple interest (Sh3,329 for Harriet) divided by this “time-interest-rate-factor” (0.47078). The answer is Sh7,071. Therefore, the bank did the calculation correctly.

Now you know the process I have to go through every time some one asks me to verify the monthly instalment for their loan. But please, don’t ask me to explain how that process is arrived at. The answer to that resides in a secondary school mathematics lesson…at least that’s where I learnt it.