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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