Question : A sum of money becomes INR 11,880 after 4 years and INR 17,820 after 6 years on compound interest, if the interest is compounded annually. What is the half of the sum (in INR)?
Option 1: 2,410
Option 2: 2,530
Option 3: 2,640
Option 4: 2,750
Correct Answer: 2,640
Solution :
Let the rate of interest per annum be $R$ and principal $P$
According to the question,
(Amount after 4 years): (Amount after 6 years) = 11880 : 17820 = 2 : 3
⇒ [$(1+\frac{R}{100})^{4}$]: [$(1+\frac{R}{100})^{6}$] = 2 : 3
⇒ $(1+\frac{R}{100})^{2}$ = $\frac{3}{2}$
Amount after 4 years = $P(1+\frac{R}{100})^{4}$
⇒ 11880 = $P(\frac{3}{2})^{2}$
⇒ P = $\frac{11880 × 4}{9}$ = 5280
⇒ $\frac{P}{2}$ = $\frac{5280}{2}$ = 2640
Hence, the correct answer is 2,640.
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