Make sure you know the interest rate on your loan
The Sunday Nation
Nairobi,
20 September 2015
I suspect that it is
out of the appreciation of the power of compounding that the
mathematical procedure of calculating the result is called “raising to
the power of”! This is what Peter Kariuki should have been aware of when
he agreed to lend Sh140,000 to a friend at a compound interest rate of
30% per month in February 2014.
Adding 30% to any
number is the same as multiplying it by 1.3; therefore, since the
interest is compounded, the loan balance (including interests earned) is
multiplied by 1.3 each month. 19 months down the line, Peter’s friend
has not paid a cent so, the loan has grown by a factor of 1.3 raised to
the power of 19.
That is:
1.3x1.3x1.3x1.3x... 19 times. This comes to 146. So, the amount owed is
now 146 x 140,000 = Sh20.44 million!
When I brought this
to Peter’s attention, he realized that the interest rate was
unreasonable and there is no way his friend will ever be able to clear
the loan. Perhaps he should consider revising the loan agreement
retroactively and state the interest rate as 30% per year, but
compounded on a monthly basis.
In that case, the
monthly interest comes to 30% divided by 12 months = 2.5%. Adding 2.5%
to any number is equivalent to multiplying by 1.025. Therefore, over 19
months, the initial amount has now grown by 1.025 raised to the power of
19; that is, 1.6 times. So, the outstanding balance is now about
Sh224,000.
This now looks more
manageable and it is probably what Peter’s friend would owe if he had
borrowed through a credit card.
*******
Isaac Nguu is also
trying to figure out how his lender is working out the interest on a
loan. In September 2011, he borrowed Sh650,000 from Equity Bank and was
supposed to pay Sh14,642 monthly for 72 months.
His August pay-slip
indicates that the loan balance is Sh366,050 while a the bank shows
Sh476,733. So the question is: which of the two is correct?
I asked Isaac what
the interest rate was and he wasn’t sure about it; but he suspected that
it was 18%. That surprised me – that one can take a loan and not be sure
what the interest rate is. Still, I worked “backwards” and established
that it was 17.5% per year, compounded monthly (commonly referred to as
“reducing balance”).
Assuming that the
first installment was made in October 2011 (out of his September salary)
and that the most recent payment was in September 2015, it turns out
that he has made 48 payments. I have done a month-by-month analysis and
found that the loan balance should be Sh294,703.
So, according to my
calculation, both the bank and the employer are wrong! The only way to
sort this out is to ask the employer and the bank to show their
month-by-month calculation of principal payments, interest and resultant
balances.
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