Question : The difference between compound interest (compounding annually) and simple interest on a sum at the rate of 30% per annum for 2 years is INR 3,600. What is the sum?
Option 1: INR 75,000
Option 2: INR 40,000
Option 3: INR 50,000
Option 4: INR 60,000
Correct Answer: INR 40,000
Solution :
Difference between compound interest (compounding annually) and simple interest = INR 3600
Rate, $R$ = 30%
Term = 2 years
Let $P$ be the principal sum.
Difference between compound interest (compounding annually) and simple interest for 2 years $=P×(\frac{R}{100})^2$
$⇒ 3600 = P×(\frac{30}{100})^2$
$⇒ 3600 = P×\frac{9}{100}$
$\therefore P = \frac{360000}{9}=40000$
Hence, the correct answer is INR 40,000.
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