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
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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