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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