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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