Question : The compound interest on a certain sum invested for 2 years at 10% per annum is INR 1,522.50, the interest being compounded yearly. The sum is:
Option 1: INR 7,250
Option 2: INR 7,200
Option 3: INR 7,500
Option 4: INR 7,000
Correct Answer: INR 7,250
Solution : Time, $n$ = 2 years Rate, $R$ = 10% Let $P$ be the sum. Compound interest, CI = INR 1,522.50 CI = $P(1+\frac{R}{100})^n - P$ ⇒ 1522.50 = $P(1+\frac{10}{100})^2 - P$ ⇒ 1522.50 = $P(1.1)^2 - P$ ⇒ 1522.50 = $1.21P- P$ ⇒ 1522.50 = $0.21P$ ⇒ $P$ = $\frac{1522.50}{0.21}$ = INR 7,250 Hence, the correct answer is INR 7,250.
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