Simple things about compound interest

These days, we regularly come across advertisements that talk about interest rates, whether in the case of loans or fixed deposits or certain other interest-bearing investments.

Very often one comes across varied interest rates offered by different entities. As a consumer, there is always a need to get the best deal -- lowest interest rate for a loan or highest earning on investment, subject to all else being equal.

If two banks with similar credentials offer different rates on their deposits, one would like to park money with the one that offers the higher rate. And that is quite natural and logical.

However, all interest rates are not equal. It is important to understand this statement as it has an implication on the final value we get on our investments.

From now on, we will restrict our discussion to investments alone, as talking about investments and loans simultaneously could be confusing.

Let us take some examples:

Let us say you are looking at investing your money for a one to one-and-a-half year period in a bank fixed deposit.

You call up your own bank and find that you can get 8 per cent for a similar period.

On the way to your bank, you see a hoarding of a bank that has just launched an aggressive campaign to mobilise fixed deposits.

The hoarding boldly announces interest rate of 9.5 per cent on your 430 days' deposit. You are tempted to go for this deposit.

However, if one probes further to do a proper comparison, one finds that there is actually no difference between both the offers. How does this happen? Well, it is all about how the rates are presented.

There is nothing wrong that any bank is doing. It is just that the presentation is different. The interest rate of 9.5 per cent is for the full 430-day period, whereas the 8 per cent interest rate is for what we call an annualised rate.

Hence, if you invest your money for a 430-day period in the deposit that gives you 8 per cent per annum, you would get Rs 10,950 (your original investment of Rs 10,000 plus interest earning of Rs 950) at the end of 430 days.

That is exactly what you get in the deposit that gives you 9.5 per cent for a 430-day deposit, if the 9.5 per cent is not an annualised rate.

For an investor, it is important to compare the investment options by looking at the various terms and nuances. Always ask for the annualised rate of interest, as that is a standard way of comparing interest rates.

Let us now move over to a longer-term deposit. Now that you ask banks for annualised rate of interest, you come across the following two options while shopping for investments.

A bank offers interest rate of 8.66 per cent per annum for a three-year deposit. There is another bank of a similar type that offers 8 per cent per annum for the same term.

Any sane person would choose the first option. However, when one reads the fine print, one gets to know that the first bank has quoted simple rate of interest whereas the second has quoted annualised rate that is also compounded annually.

This means, the investor in the first case gets interest at 8.66 per cent every year on the amount invested.

Over three years, the total earning would be around Rs 2,597 for a deposit of Rs 10,000. However, the deposit that gives you 8 per cent per annum compounded annually would allow you to earn 8 per cent per annum on your investment as well as on the interest thereon.

The total earning in this case also would also be Rs 2,597 if you deposited Rs 10,000. Once again, both the banks are right when they quote their deposit rates. The only thing the first bank did not tell you is that you are not earning interest on your interest or there is no compounding effect.

It is always necessary to ask for compounded annualised interest rate when you are considering an interest bearing investment.

The discussion here has been limited to an assumption that the investment options that one is considering are sound and that the chances of loss are very low. The risk component adds another dimension to the whole equation of selecting your investment options.