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?

Answer 1

Let the amount borrowed by Amit is $x,$

Compound Interest $-$ Simple Interest $=$ Gain

$x\left[{\left(1+\frac{8}{100}\right)}^2-1\right]-\frac{x\times 8\times 2}{100}=16$

$\Rightarrow 0.1664x-0.16x=16$

$\Rightarrow x=\frac{16}{0.0064}$

$\Rightarrow x=\text{Rs.}2500$