Question : A sum of INR $x$ amounts to INR 12,777.60 in 2 years at INR 15% p.a., when the interest is compounded for eight months. The value of $x$ is _____.
Option 1: INR 9800
Option 2: INR 10400
Option 3: INR 9600
Option 4: INR 10200
Correct Answer: INR 9600
Solution :
Amount = $P(1+\frac{r}{100n})^{nt}$, where
$P$ = Principal
$r$ = rate = 15%
$t$ = time = 2 years
$n$ = period = $\frac{12}{8}$ = $\frac{3}{2}$
Now,
⇒ 12777.60 = $P(1+\frac{10}{100})^{3}$
⇒ $P = 12777.60 ×(\frac{10}{11}) × (\frac{10}{11}$) × ($\frac{10}{11})$ = 9600
Hence, the correct answer is INR 9600.
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