How to calculate compound interest on savings

Githuku Mungai says that his Chama (self-help group) has been offered different savings accounts by two banks. Bank A is offering 7 per cent interest per annum compounded daily. while bank B is also promising 7 per cent  per annum but compounding monthly. His request is: “Please compare Sh1 million for A and B (please remember there is 15 per cent withholding tax deducted).”

Compounded interest means that the amount earned in a period also earns interest. Bank B is more typical in the industry. Banks like to work on a monthly system because most people get paid in the same cycle.

Thus to work out the annual interest for Bank B, we first divide the interest rate by 12. This gives 0.5833 per cent per month. Therefore, at the end of the first month, the Sh1,000,000 earns Sh5,833. The new balance in the account goes up to Sh1,005,833.

During the second month, this new balance (Sh1,005,833) earns the 0.5833 per cent interest, or Sh5,867. The new balance comes to Sh1,011,700. We notice that the earning now is higher than the previous one even though we are applying the same rate. That’s the secret of compounded interest.

Now, we have seen that when 0.5833 per cent is added to Sh1,0000,000, the resultant balance is Sh1,005,833. Thus doing so is equivalent to multiplying the initial balance by 1.005833.

This means that, to get the balance at the end of a month, we simply multiply by 1.005833. Thus at the end of the first month, the balance is Sh1,000,000 x 1.005833 = Sh1,005,833; and at the end of the second month, it is Sh1,005,833 x 1.005833 = Sh1,011,700.

Now let’s stop and do a review. What we have actually done in the second month is Sh1,000,000 x 1.005833 x 1.05833. By the same logic, the balance at the end of the third month should be Sh1,000,000 x 1.005833 x 1.005833 x 1.005833. In other words; 1.005833 cubed.  Therefore, at the end of one year (12 months) the balance will be Sh1,000,000 multiplied by 1.005833 raised to the power 12. The answer is Sh1,072,290.

What about the withholding tax? The 15 per cent is charged on the interest earned each month; that is, on the 7 per cent. Now; 15 per cent of 7 is 1.05. So, the net interest earned after tax is (7 – 1.05) per cent = 5.85 per cent. Going through the same steps as before using the net rate, the actual true balance at the end of one year is Sh1,061,150.

For bank A, the compounding is done daily, thus to find the annual returns we must first divide the 7 per cent rate by 365. This comes to 0.01918 per cent per day. When we subtract the withholding tax, the net daily return comes to 0.01630 per cent.

Using the same steps as before, it turns out that the annual factor is 1.0001630 raised to the power of 365. The result is 1.061301. Therefore, Sh1,000,000 invested for one year in Bank B will increase to Sh1,061,300 in one year. This is just Sh150 more than Bank A. In my view, the choice should be based on something else other than the returns.

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