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On what sum of money will the difference between simple interest and compound interest for 2 years at 5% per annum be equal to Rs. 63 ?

a) Rs. 24600
b) Rs. 24800
c) Rs. 25200
d) Rs. 25500

Answer: c
Explanation:
$$\eqalign{ & {\text{Rate of interest = 5}}\% {\text{ per annum}} \cr & {\text{Time = 2 year}} \cr & P\left[ {{{\left( {1 + \frac{r}{{100}}} \right)}^n} – 1} \right] – \frac{{P \times r \times t}}{{100}}{\text{ = 63}} \cr & P\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^2} – 1} \right] – \frac{{P \times 5 \times 2}}{{100}}{\text{ = 63}} \cr & P\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^2} – 1} \right] – \frac{{10P}}{{100}}{\text{ = 63}} \cr & P\left[ {{{\left( {\frac{{105}}{{100}}} \right)}^2} – 1} \right] – \frac{{10P}}{{100}}{\text{ = 63}} \cr & P\left( {\frac{{11025 – 10000}}{{10000}}} \right) – \frac{{10P}}{{100}} = 63 \cr & \frac{{1025P}}{{10000}} – \frac{{10P}}{{100}} = 63 \cr & \frac{{1025P – 1000P}}{{10000}} = 63 \cr & 25P = Rs.630000 \cr & P = \frac{{630000}}{{25}} \cr & P = Rs. 25200 \cr} $$

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