Effective Interest Rate
Effective Interest Rate
Let i be the nominal interest rate compounded
annually. But, in practice, the compounding may occur less than a year. For
example, compounding may be monthly, quarterly, or semi-annually. Compounding
monthly means that the interest is computed at the end of every month. There
are 12 interest periods in a year if the interest is compounded monthly. Under
such situations, the formula to compute the effective interest rate, which is compounded
annually, is
Effective
interest rate, R = (1 + i/C)C −1
where,
i = the
nominal interest rate
C = the
number of interest periods in a year.
The future maturity value at the end of the
“n” years is,
F = P (1
+ R)n
Example problem on effective interest rate
Mr John deposits a sum of Rs. 15,000 in a
bank at a nominal interest rate of 6 % for 8 years. The compounding is quarterly.
Find the maturity value of the deposit after 8 years.
Given data
P = Rs.
15,000
i = 6%
n = 8
years
C = 12/3
= 4
To find
R, F
Formula used
R = (1 +
i/C)C −1
F = P (1
+ R)n = P (F/P,
R, n)
Solution
R = (1 + i/C)C −1
=
(1 + (6/100)/4)4 −1
=
6.14%
The future maturity value at the end of the 8
years is,
F = P (1 + R)n
= 15,000
[1 + (6.14/100)]8
= 15,000
(1.61076)8
F = Rs. 24161.50
Result
The
future maturity value at the end of the 8 years is Rs. 24161.50.
