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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