Question : On a certain sum, the simple interest for 2 years is INR 12000. If the sum is INR 12000, then what will be the compound interest (compounding annually) on the same sum at the same rate of interest for the first 3 years?
Option 1: INR 29250
Option 2: INR 29300
Option 3: INR 28500
Option 4: INR 22750
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Correct Answer: INR 28500
Solution : Sum, $P$ = INR 12000 Simple interest, SI = INR 12000 Term, $n$ = 2 years Let $R$ be the interest rate. Simple interest = $\frac{\text{Principal × term × Rate}}{100}$ ⇒ $12000 = \frac{12000 × 2 × R}{100}$ ⇒ $R = \frac{100}{2} = 50$% Term, $n$ = 3 years When compounded annually, Compound interest = $P(1+\frac{R}{100})^n - P$ = $12000(1+\frac{50}{100})^3 - 12000$ = $12000(1+\frac{1}{2})^3 - 12000$ = $12000(\frac{3}{2})^3 - 12000$ = $12000(\frac{27}{8} - 1)$ = $12000×\frac{19}{8}$ = $28500$ Hence, the correct answer is INR 28500.
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