The effective rate that is equivalent to a nominal rate of 6% per annum compounded semi-annually is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 6.09%
For a nominal rate r compounded m times a year, the effective annual rate is
\( \displaystyle r_{\text{eff}}=\left(1+\frac{r}{m}\right)^m-1 \)
Here r = 0.06 and m = 2:
\( r_{\text{eff}}=(1.03)^2-1 \)
\( r_{\text{eff}}=1.0609-1=0.0609=6.09\% \)
Tip: The effective rate is always a little more than the nominal rate when interest is compounded more than once a year; any option below or equal to the nominal rate can be ruled out.
CBSE Applied Mathematics (Class XII):
Nominal and Effective Rate of Interest
