How to turn a compound interest loan into a simple interest one

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

10 September 2017

An anonymous reader wants to know: “If I borrow Sh1,000 with a 7.5% interest per month, how much will I pay after 3yrs” The answer is not straightforward. It depends on how the interest is calculated.

If you stay with the money for the three years without paying a penny, there are two ways of working out the total interest. First is assuming simple interest; that is, you are not charged interest on interest.

In such a case, we calculate the monthly interest and then multiply by 36 months. 7.5% of Sh1,000 is Sh75; in 36 month, this come to Sh75 x 36 = Sh2,700. This is then added to the Sh1,000 that was borrowed and the total is Sh3,700.

The second method is when the interest is compounded. At the end of the first month, you will owe Sh1,075. At the end of the second month, 7.5% will be added to the entire Sh1,075. Therefore, the new balance comes to Sh1,156.

When this is repeated monthly for three years (36 months), the final balance will be Sh13,512! This is much higher than the Sh3,700 from the simple interest method. So, one might wonder whether there is a way to stop this runaway accumulation of the debt.

The answer is yes. You can stop the accumulation by paying the interest earned every month; that is, Sh75. That way, you ensure that the money owed never exceeds the Sh1,000 that you borrowed.

When you think about it, doing this will automatically convert the compound interest into simple interest! The total repayment will come to Sh3,700.

My only concern about this loan is this: why is the interest rate so high? 7.5% per month is equivalent to 90% per year!

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Some questions never seem to go away. The one about a person spending Sh500 in small amounts resurfaced this week. He adds up the balances remaining after each expense and, of course, the total is more than Sh500. So he wonders where the extra comes from. If you come across the puzzle, just ask yourself why the balances are being added. Nobody does that!

Another question that resurfaced is the one about a small car moving at 50km/h compared to a bus also moving at 50km/h. Shouldn’t the bus be faster since it has larger wheels?

I have discovered a good away of explaining this one. It involves understanding the fact that 50km/h means traveling 50km in one hour. With that in mind, we can break the question into two.

First: is a distance of 50km longer when measured while in the bus than when in a small car? That sounds ridiculous, doesn’t it? 50km is 50km where ever you measure it from.

Second: is one hour a shorter duration when measured in a moving bus than when in the small car? Again, that’s an absurd suggestion! Therefore, there is no reason to expect that a bus doing 50km/h will be faster than a small car travelling at 50km/h.