GATE 2024 CE (CE2) – Question 47
The expression for computing the effective interest rate ($i_{eff}$) using continuous compounding for a nominal interest rate of 5% is $i_{eff} = \lim_{m \to \infty}\left(1 + \frac{0.05}{m}\right)^m - 1$
The effective interest rate (in percentage) is ____________ (rounded off to 2 decimal places).
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Show answer and explanation
Correct answer: 5.10 to 5.16
Explanation
The limit is $\lim_{m \to \infty}\left(1 + \frac{r}{m}\right)^m = e^r$. So $i_{eff} = e^{0.05} - 1 = 1.05127 - 1 = 0.05127$, which is 5.13%.