The effective rate that is equivalent to a nominal rate of 6% compounded semi-annually is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6.09%
The effective rate for a nominal rate i compounded m times a year is
\( \displaystyle r_{\text{eff}} = \left(1 + \frac{i}{m}\right)^m - 1 \)
Here i = 0.06 and m = 2:
\( \displaystyle r_{\text{eff}} = \left(1 + \frac{0.06}{2}\right)^2 - 1 \)
\(= (1.03)^2 - 1\)
\(= 1.0609 - 1 = 0.0609\)
So the effective rate is 6.09%.
CBSE Applied Mathematics (Class XII):
Nominal and Effective Rate of Interest
