How to calculate returns from an investment

After reading the column of May this year where I advised against keeping savings in a bank account, Robert Mutemi pulled out his money and opened a Money Market Fund Unit Trust with one of the insurance companies.

He writes, “I started with Sh10,000 on September 3 and then on the 15th I added another Sh20,000. Later on the 25th I added Sh100,000 more.

“In total, I have put in Sh130,000. Recently, I got my statement for the month of September and it shows that the total interest earned was Sh355.35. My balance is now Sh130,355.35. I know that they publish the daily interest in the papers but it is difficult to keep a record every day. How can I calculate the combined interest rate for my savings?”

Robert’s problem would have been easy had he deposited the entire Sh130,000 on the same day – September 3. In that case, we would have divided Sh355.35 by Sh130,000 and converted the answer to a percentage. That is, 0.273 per cent.

But since this is for only 27 days (from the 3rd to the 30th), it needs to be converted to an annual value. To do that, we divide 0.273 by 27 and multiply the result by 365; the answer is 3.69 per cent.

AVERAGE BALANCE

Now, if this money was in a bank savings account, 3.69 per cent per annum would be a very decent return. But it wasn’t: it was in a unit trust where returns are much better. So, there is something wrong with that calculation.

We must account for the fact that the different amounts were deposited on different days. That is, we need to find out the average balance for the 27 days that the money has been invested.

To get that, we start by multiplying the account balances by the number of days. That is, Sh10,000 was in the account for 12 days (3rd to 15th) so, 10,000 x 12 = 120,000. From there the balance rose to Sh30,000 (after adding Sh20,000). The Sh30,000 stayed in the account for 10 days, so 30,000 x 10 = 300,000. Finally, the balance shot up to Sh130,000 and this remained there for 5 days to the end of the month. So, 130,000 x 5 = 650,000.

Next we add up all these products: that is, 120,000 + 300,000 + 650,000 = 1,070,000. Finally, we divide this result by the total number of days, that is, 1,070,000 / 27 = 39,630.

So, Robert’s three transaction on the three separate days were equivalent to depositing Sh39,630 and keeping it there for 27 days. This is the effective amount that earned the Sh355.35. So the rate of return is 355.35 divided by 39,630 = 0.897 per cent.

But this must be converted to an annual rate; thus, we divide it by 27 and multiply the result by 365. The answer is 12.12 per cent. Finally, we must also account for the fact that interest earned attracts withholding tax at the rate of 15 per cent. So we divide the 12.12 per cent by 0.85 to get the gross rate of return. The answer is 14.26 per cent.

Now, even if you haven’t followed the full working, you must ask yourself whether the bank could have paid Robert Sh355 for such deposits within one month. I don’t think so; I suspect he would have gotten about Sh17 – yes, seventeen bob!