Question : The compound interest amounts on a certain sum at a certain rate percentage p.a. for the second year and third year are INR 3,300 and INR 3,630, respectively. What is the amount of the same sum at the same rate in $2 \frac{1}{2}$ years, interest compounded yearly?
Option 1: INR 37,215
Option 2: INR 36,300
Option 3: INR 38,115
Option 4: INR 36,000
Correct Answer: INR 38,115
Solution :
Compound Interest (CI) for 2nd year = INR 3300
CI for 3rd year = INR 3630
Interest rate = $\frac{(\text{CI of 3rd year} – \text{CI of 2nd year})}{\text{CI of 2nd year}}$ × 100%
⇒ Interest rate = $\frac{(3630 – 3300)}{3300}$ × 100 = 10%
CI for first year = $\frac{3300 × 100}{110}$ = 3000
Let Principal be P, then
10% of P = 3000
⇒ P × $\frac{1}{10}$ = 3000
⇒ P = 30,000
So, the total interest for $2\frac{1}{2}$ years = CI for 1st year + CI for 2nd year + $\frac{\text{CI for 3rd year}}{2}$
= 3000 + 3300 + $\frac{3630}{2}$
= 3000 + 3300 + 1815 = 8115
Amount after $2\frac{1}{2}$ years = 30,000 + 8115 = 38,115
Hence, the correct answer is INR 38,115.
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