Question : The compound interest (compounding annually) on a certain sum for 2 years at the rate of 60% per annum is INR 6240. What will be the simple interest on the same sum for 3 years at the same rate of interest?
Option 1: INR 6800
Option 2: INR 7200
Option 3: INR 7100
Option 4: INR 6500
Correct Answer: INR 7200
Solution :
Rate, $R$ = 60%
Term, $n$ = 2 years
Compound interest = INR 6240
Let $P$ be the principal sum.
When compounded annually,
Compound interest = $P(1+\frac{R}{100})^n - P$
$⇒6240 = P(1+\frac{60}{100})^2 - P$
$⇒6240 = P(1+\frac{3}{5})^2-P$
$⇒6240 = P(\frac{8^2}{5^2})-P$
$⇒6240 = P(\frac{64}{25}-1)$
$⇒6240 = P×\frac{39}{25}$
$⇒P = \frac{6240×25}{39}$
$\therefore P = 4000$
Now, $ n = 3$ years
Simple interest = $\frac{PnR}{100}=\frac{4000 × 3 × 60}{100}= 7200$
Hence, the correct answer is INR 7200.
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