Question : If the difference between the compound interest and simple interest on a certain sum of money for 3 years at the rate of 4% per annum is INR 76, then what is the sum?
Option 1: INR 16,725
Option 2: INR 12,925
Option 3: INR 15,625
Option 4: INR 18,825
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Correct Answer: INR 15,625
Solution :
Given: Compound interest – Simple interest = 76
Rate, $R$ = 4%
Let the sum be $P$.
$P(\frac{R}{100})^{2}(3 +\frac{R}{100})=76$
⇒ $P(\frac{4}{100})^{2}(3+\frac{4}{100})=76$
⇒ $P(\frac{1}{625})(\frac{76}{25})=76$
$\therefore P=15625$
Hence, the correct answer is INR 15,625.
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