The effective rate corresponding to 8.4% compounded monthly is [ Given \( (1.007)^{12}\approx 1.087 \) ]
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 8.7% per annum
The effective rate is the rate which, compounded once a year, gives the same amount as the nominal rate compounded m times a year:
\( \displaystyle r_{\text{eff}}=\left(1+\frac{r}{m}\right)^m-1 \)
Here r = 8.4% = 0.084 and m = 12, so the monthly rate is \( \frac{0.084}{12}=0.007 \):
\( \displaystyle r_{\text{eff}}=(1.007)^{12}-1 \)
\( \displaystyle \approx 1.087-1=0.087 \)
So the effective rate is 8.7% per annum.
CBSE Applied Mathematics (Class XII):
Nominal and Effective Rate of Interest
