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Question

Amit borrowed a certain sum of money for $$2$$ years at $$8\%$$ per annum on simple interest and immediately lent it to Ravi but at compound interest and gained $$\text{Rs. } 16$$. What amount did Amit borrow?


Solution

Let the amount borrowed by Amit is $$x,$$
Compound Interest $$-$$ Simple Interest $$=$$ Gain
$$x\left[ {{{\left( {1 + \dfrac{8}{{100}}} \right)}^2} - 1} \right] - \dfrac{{x \times 8 \times 2}}{{100}} = 16$$
$$ \Rightarrow 0.1664x - 0.16x = 16$$
$$ \Rightarrow x = \dfrac{{16}}{{0.0064}} $$
$$\Rightarrow x=\text{Rs. }2500$$

Mathematics

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