Question : What is the compound interest on a sum of INR 37,500 for $1 \frac{1}{3}$ years at a rate of 12% p.a. if the interest is compounded 8 - monthly?
Option 1: INR 6,420
Option 2: INR 6,448
Option 3: INR 6,240
Option 4: INR 6,440
Correct Answer: INR 6,240
Solution :
Amount = $P(1+\frac{r}{100})^{t}$
$P$ = Principal
$r$ = rate
$t$ = time
According to the question,
$r$ = $\frac{12}{12}$ × 8 = 8% per 8-months
$t$ = $\frac{16}{8}$ = 2 terms
Now,
⇒ Amount $= 37500 × (1+\frac{8}{100})^{2} = 37500 × (\frac{27}{25}) × \frac{27}{25} = 43740$
$\therefore$ Compound interest = 43740 – 37500 = 6240
Hence, the correct answer is INR 6,240.
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