The effective rate that is equivalent to a nominal rate of 12% compounded quarterly is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 12.55%
For a nominal rate i compounded m times a year, the effective rate is the interest actually earned on Rs. 1 in one year:
\( \displaystyle r_{\text{eff}} = \left(1+\frac{i}{m}\right)^m - 1 \)
Here i = 0.12 and m = 4 (quarterly):
\( \displaystyle r_{\text{eff}} = \left(1+\frac{0.12}{4}\right)^4 - 1 \)
\(= (1.03)^4 - 1\)
\(= 1.12550881 - 1\)
\(\approx 0.1255\)
So the effective rate is about 12.55%.
CBSE Applied Mathematics (Class XII):
Nominal and Effective Rate of Interest
