Converting loan interest rate from fixed to reducing balance
The Sunday Nation
Nairobi,
14 October 2012
In last week’s article, we found that there is no constant conversion factor for changing the monthly instalments of a loan from reducing balance to fixed interest rate. After reading the analysis, Daniel Mbuvi was not satisfied with the answer. Hence he wrote:
“You did not answer the question that your reader had asked. I think he wanted to know if there is a way one can convert the interest rate itself from [the] reducing balance to [the] fixed type… Can you analyse that one as well?”
Here goes…
In the previous article, we found that if you take a Sh100,000 loan at 10 per cent per annum for five years on reducing balance, you would pay back Sh2,125 per month. Now the question that Daniel is asking is this: what would be the fixed interest rate that gives the same monthly instalments?
In the fixed rate method of calculation, the interest is calculated on the total amount borrowed for the full period of the loan and then added to the principal. The resulting sum is then divided by the number of months to get the monthly instalment.
Therefore, our first step is to find out the total amount repaid. At Sh2,125 per month over five years (60 months), you end up paying back Sh127,500 altogether. That is, the total interest over the term of the loan is only Sh27,500 – remember, you had borrowed Sh100,000.
This Sh27,500 is distributed equally over the fiver years. Thus the interest amount per year is Sh5,500 (27,500 divided by five); and therefore the fixed interest rate comes to 5.5 per cent (Sh5,500 divided by Sh100,000).
In other words, for this specific example, 10 per cent on reducing balance is equivalent to 5.5 per cent on fixed interest method. The conversion factor is 5.5 divided by 10, that is, 0.55.
Let’s see what happens if the interest rate is raised to 20 per cent (leaving all other factors constant). In that case, the monthly instalment on the reducing balance method is Sh2,649 per month. Notice that even though the rate has double, the repayment amount increase by a much smaller proportion – from Sh2,125 to Sh2,649. For that reason, I do not expect the conversion factor to be the same as before; but let’s find out…
At Sh2,649 monthly, the total repayment comes to Sh158,940; therefore the interest rate using the fixed method comes to 11.788 per cent. Thus the conversion factor is now 11.8 divided by 20; which is 0.589 – quite different from the 0.55 from the first case.
If the term of the loan changes from five to ten years and the interest rate held at 10 per cent, the reducing balance method yields a monthly instalment of Sh1,322. Consequently; the conversion factor comes to 0.586. The difference between the last two results is small, but it is still a difference!
Therefore, we can conclude confidently that there is no constant conversion factor for changing a fixed interest rate to reducing balance. But what about the formula…?
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