Question : If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, the compound interest on the same at the same rate and for the same time is:
Option 1: Rs. 50.50
Option 2: Rs. 51.25
Option 3: Rs. 51.50
Option 4: Rs. 51.05
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Correct Answer: Rs. 51.25
Solution : Let the amount be Rs. $x$ Simple Interest on Rs. $x$ for 2 years and 5% interest = Rs. 50 Simple Interest on Rs. $x$ for t years and r% interest = $\frac{{x\times r}\times t}{100}$ So, $50 = \frac{{x\times 5}\times 2}{100}$ ⇒ $x = 500$ Compound Interest on Rs. $x$ with $r%$ rate for $t$ years = $x\left (1+\frac{r}{100} \right )^{t}-x$ = $500\left (1+\frac{5}{100} \right )^{2}-500$ = Rs. 51.25 Hence, the correct answer is Rs. 51.25.
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