Question : The simple interest on a sum of money at 10% per annum for 2 years is INR 8,100. What would be the compound interest (in INR) on the same sum for the same period at 15% p.a, when the interest is compounded yearly? (nearest to INR 1)
Option 1: 8,100
Option 2: 12,751
Option 3: 14,671
Option 4: 13,061
Correct Answer: 13,061
Solution : Rate, $R$ = 10% Term, $n$ = 2 years Simple interest = INR 8,100 Let $P$ be the principal sum. Simple interest, SI = $\frac{\text{Principal×term×Rate}}{100}$ ⇒ 8100 = $\frac{P × 2 × 10}{100}$ ⇒ $P=\frac{81000}{2}$ ⇒ $P=40500$ and, $R=15$% Compound interest, CI = $P(1+\frac{R}{100})^n-P$ = $40500(1+\frac{15}{100})^2-40500$ = $53561.25-40500$ =$13061.25$ ~ $13061$ Hence, the correct answer is 13,061.
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