The effective rate per annum equivalent to a nominal rate of 8% compounded semi-annually is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 8.16%
The effective rate equivalent to a nominal rate i compounded m times a year is
\( \displaystyle r_{\text{eff}} = \left(1 + \frac{i}{m}\right)^m - 1 \)
Here \(i = 0.08\) and \(m = 2\) (semi-annually):
\( \displaystyle r_{\text{eff}} = \left(1 + \frac{0.08}{2}\right)^2 - 1 \)
\(= (1.04)^2 - 1 = 1.0816 - 1 = 0.0816\)
So the effective rate is 8.16% per annum.
CBSE Applied Mathematics (Class XII):
Nominal and Effective Rate of Interest
