Question : At what rate percent per annum will a sum of INR 15, 625 amount to INR 21, 952 in three years, if the interest is compounded annually?
Option 1: 12%
Option 2: 8%
Option 3: 9%
Option 4: 10%
Correct Answer: 12%
 
  Solution :
 
 Principal (P) = INR 15, 625
 
  Time (T) = 3 years
  
  Amount (A) = INR 21, 952
  
  Amount = $P(1 + \frac{R}{100})^T$
  
  Let the rate of interest per annum be $R$.
  
  21952 = 15625$(1 + \frac{R}{100})^3$
  
  ⇒ $\frac{21952}{15625} = (1 + \frac{R}{100})^3$
  
  ⇒ $\sqrt[3]{(\frac{21952}{15625})} = 1 + \frac{R}{100}$
  
  ⇒ $\frac{28}{25} = 1 + \frac{R}{100}$
  
  ⇒ $\frac{28}{25} - 1 = \frac{R}{100}$
  
  ⇒ $R = (\frac{3}{25}) \times 100$
  
  ⇒ $R = 3 \times 4$
  
  ⇒ $R = 12\%$
  
  $\therefore$ The rate percent per annum is 12%.
  
  Hence, the correct answer is 12%.
 
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