It is easy to calculate mortgage payments for yourself, but…

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

09 December 2007

In the science fiction movie (and book), 2001: A Space Odyssey, the author, Arthur C. Clark, dreamed up a fictitious supercomputer called the “HAL”. Then some bright spark realized that the letters “H – A - L” are all one step ahead of “I – B - M” in the alphabetical order.

Even though Arthur Clark denied that the name was intended to be ahead of IBM – the computer manufacturer – the chances of it being a coincidence are small; one in 17,576 (26 x 26 x 26)!

I remembered that story because I received a question about money from a person called John Lipesa. Now what are the odds of that? It’s very hard to calculate, but it must be lower than one in 17,576! Nonetheless, John’s question is this: “How do you calculate mortgage [payments]? We could not be taught in high school as it was said to be out of the syllabus.”

To calculate mortgage payments, one needs to know three things: the loan amount, the interest rate applicable and the duration for repaying. Most financial institutions use the so-called “reducing balance” method in their computations.

Suppose you borrow Sh1,000,000 to be paid back in 10 years at an interest rate of 12 percent per annum. The interest is calculated on a monthly basis and, in this case, it is one percent per month.

Thus on the first month, the interest alone will be Sh10,000. If you pay anything les than this figure, your balance will be greater than the amount you borrowed! Suppose you pay Sh15,000. Only Sh5,000 will go towards clearing the loan. Thus your balance will be Sh995,000.

On the second month, interest will be calculated on the Sh995,000 balance – the result is Sh9,950. If you pay another Sh15,000, then Sh5,050 will go towards clearing the loan. Notice that this figure is greater (albeit slightly) than that of the first month. If you continue this way, you will finish the paying in nine years and two months.

But usually, the bank doesn’t want to work with such awkward figures: It prefers rounded values like, 10 years. If you are going to be allowed ten years instead of nine, it is obvious that the monthly installment will be slightly lower than Sh15,000.

To get the actual answer, one sets up an equation along the steps demonstrated above but this time, the monthly installment is the unknown quantity – the loan amount (Sh1,000,000), interest rate (12 percent per year, or one percent per month) and duration of payment (10 years, or 180 months) are all known.

The result is an easy to use formula that is not easy to reproduce on this page. And after plugging the know quantities, the answer comes out as Sh14,347.09 per month. But if, like most people, you are only interested in results, then send me the known values and I will work out the unknown for you.