How to calculate returns from an investment
The Sunday Nation
Nairobi,
11 October 2015
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.
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 earner 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!
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