Question : The interest accrued on INR 12,000 in two years, when interest is compounded annually, is INR 3,870. What is the rate of interest per annum?
Option 1: 12.5%
Option 2: 10%
Option 3: 20%
Option 4: 15%
Correct Answer: 15%
Solution :
Principal sum, $P$ = INR 12,000
Term, $n$ = 2 years
Compound interest = INR 3870
Let $R$ be the interest rate.
When compounded annually,
Compound interest = $P(1+\frac{R}{100})^n - P$
⇒ $3870 = 12000(1+\frac{R}{100})^2 - 12000$
⇒ $3870 + 12000 = 12000(1+\frac{R}{100})^2 $
⇒ $\frac{15870}{12000} = (1+\frac{R}{100})^2$
⇒ $\frac{529}{400}= (1+\frac{R}{100})^2$
⇒ $\frac{23}{20}= 1+\frac{R}{100}$
⇒ $\frac{23-20}{20} = \frac{R}{100}$
⇒ $R = 3 × 5 = 15$%
Hence, the correct answer is 15%.
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