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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