The effective rate \( r_{e} \) corresponding to the nominal rate r compounded continuously is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( e^{r}-1 \)
The effective rate is the actual interest earned on Rs. 1 in one year. At nominal rate r compounded m times a year, Rs. 1 grows to \( \left(1+\frac{r}{m}\right)^{m} \). Under continuous compounding m → ∞:
\( \displaystyle \lim_{m\to\infty}\left(1+\frac{r}{m}\right)^{m}=e^{r} \)
So the interest on Rs. 1 in one year is
\( r_{e}=e^{r}-1 \)
CBSE Applied Mathematics (Class XII):
Nominal and Effective Rate of Interest
