For an investment, if the nominal rate of interest is 10% compounded half yearly, then the effective rate of interest is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 10.25%
The effective rate is the rate that, compounded once a year, gives the same growth. Half-yearly compounding at 10% means 5% for each of the 2 half-years:
\( \displaystyle r_{\text{eff}} = \left(1 + \frac{0.10}{2}\right)^{2} - 1 \)
\(= (1.05)^2 - 1 = 1.1025 - 1 = 0.1025\)
The effective rate is 10.25%.
CBSE Applied Mathematics (Class XII):
Nominal and Effective Rate of Interest
