What is compound interest?

Albert Einstein described compound interest as the eighth wonder of the world, saying: “Those who understand it, earn it… those who don’t pay it.”

The simplest explanation is that compound interest is when you earn or pay interest on your interest.

For example, if you deposit or borrow a sum of money, say R10 000, at an interest rate of 10% per annum in the first month the interest will be based on the R10 000. In the second month, it is calculated on the R10 000 plus the interest you have earned. In the third month on the R10 000 plus the interest you have earned in the two preceding months and so on. In a table the compounding effect looks like this.

Sound complicated?

One way to understand the power of compounding is to think about the Chinese legend of rice on a chess board. The story goes that when the inventor of chess demonstrated the game to the emperor, the ruler was so impressed he asked him to name his reward. The man asked for a grain of rice to be placed on the first square of the board, two on the next, four on the next, eight on the next, with the quantity doubling every time for each of the 64 squares. The sum-total of all the rice would come to 18 446 744 073 709 551 615, much more than most people expect.

This compounding effect can be very beneficial if you’re saving or investing money. By earning interest on the interest you’re compounding your original investment. Based on the example above, after a year you’ll have earned R1 047,13 on your original investment of R10 000.

But, if you’ve borrowed money, the compounding works against you, because you’re paying interest on the original amount plus the interest that is added each month. That’s one of the reasons that it’s never a good idea to miss a repayment instalment on a loan – the interest will compound and you’ll end up paying more than the original instalments. You might also be subject to penalties and missing payments will probably impact your credit score.

How to calculate compound interest

There are plenty of online tools that will help you work out compound interest over a given period, such as the loan repayment calculator. 

If you’d prefer to do the calculations yourself the compound interest formula is A = P (1 + r/n) ^(nt)

‘A’ is the final amount, ‘P’ is the principal sum you’ve invested or borrowed, ‘r’ is the interest rate, ‘n’ is the number of compounding periods (months) in a year and ‘t’ is the time period in years.

What’s more important than knowing how to work out compound interest is appreciating the principle and the effect it can have on your financial situation. Understanding this enables you to make sound financial decisions.