Question : The difference between the simple and compound interest on a certain sum of money at an $8\%$ rate of interest per annum for two years is INR 56. Find the sum.
Option 1: INR 8750
Option 2: INR 7058
Option 3: INR 7805
Option 4: INR 8057
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Correct Answer: INR 8750
Solution :
The difference between compound interest and simple interest for two years $\mathrm{= \frac{P \times R^2}{100^2}}$
where $\mathrm{P}$ is the principal amount (the sum of money) and $\mathrm{R}$ is the rate of interest.
Given that the difference is INR 56 and the rate of interest is $8\%$.
$56 = \mathrm{\frac{P \times 8^2}{100^2}}$
$⇒\mathrm{P} = \frac{56\times 100^2}{8^2} = \frac{560000}{64} = 8750$
Hence, the correct answer is INR 8750.
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