The effective rate that is equivalent to a nominal rate of 8% compounded continuously is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( (e^{0.08}-1)\times 100\ \% \)
For a nominal rate r compounded continuously, Rs. 1 grows to \( e^{r} \) in one year. The effective rate is the actual gain in one year:
\( \displaystyle r_{\text{eff}}=e^{r}-1 \)
With r = 8% = 0.08:
\( \displaystyle r_{\text{eff}}=(e^{0.08}-1)\times 100\% \)
Why the other options are incorrect
Option (1) \( (e^{8}-1)\times 100\ \% \) — Incorrect. The rate must be used as a decimal, 0.08, not as 8.
Option (2) \( e^{0.08}\times 100\ \% \) — Incorrect. \( e^{0.08} \) is the amount of Rs. 1 after a year; the principal 1 must be subtracted to get the rate.
Option (4) \( \left(\left(1+\displaystyle\frac{0.08}{12}\right)^{12}-1\right)\times 100\% \) — Incorrect. This is the effective rate for monthly compounding, not continuous compounding.
CBSE Applied Mathematics (Class XII):
Nominal and Effective Rate of Interest
