The effective rate which is equivalent to stated rate of 6% compounded semiannually is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 6.09%
A stated (nominal) rate r compounded m times a year has the effective rate
\( \displaystyle r_{\text{eff}} = \left(1 + \frac{r}{m}\right)^{m} - 1 \)
Here r = 0.06 and m = 2:
\( \displaystyle r_{\text{eff}} = (1.03)^{2} - 1 \)
\(= 1.0609 - 1 = 0.0609\)
So the effective rate is 6.09%. It is a little more than 6% because the interest of the first half-year also earns interest in the second half.
CBSE Applied Mathematics (Class XII):
Nominal and Effective Rate of Interest
