Question : If interest is being compounded half-yearly, then what sum will amount to INR 51,840 in 2 years at the rate of 40% per annum on compound interest?
Option 1: INR 25,000
Option 2: INR 15,000
Option 3: INR 20,000
Option 4: INR 30,000
Correct Answer: INR 25,000
Solution :
Amount = INR 51,840
Term, $n$ = 2 years
Rate, $R$ = 40%
Let $P$ be the principal sum.
When compounded half-yearly,
Amount = $P(1+\frac{R}{200})^{2n}$
⇒ 51840 = $P(1+\frac{40}{200})^{2×2}$
⇒ 51840 = $P(1+\frac{1}{5})^{4}$
⇒ 51840 = $P(\frac{6}{5})^{4}$
⇒ $P = \frac{51840×625}{36×36}=25000$
Hence, the correct answer is INR 25,000.
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