Question

A sum of money is lent at 8% per anuum compound interest. If the interest for the second year exceeds that for the first year by Rs. 96, find the sum money.

Answer 1

Let P=Rs x,R=8% then

Then interest for the first year=$\frac{x\times 8\times 1}{100}=\frac{8x}{100}$

Then Principal foe the second year=$x+\frac{8}{100}x=Rs\frac{108}{100}x$

hence interest for the second year$=\frac{\frac{108}{100}x\times 8\times 1}{100}=Rs.\frac{864x}{10000}$

According to the question

$\Rightarrow \frac{864x}{10000}=\frac{8x}{100}+96$

$\Rightarrow \frac{864x}{10000}-\frac{8x}{100}=96$

$\Rightarrow \frac{864x-800x}{10000}=96$

$\Rightarrow \frac{64x}{10000}=96$

$\Rightarrow 64x=96\times 10000$

$\Rightarrow x=\frac{96\times 10000}{64}$

$\Rightarrow x=15000$

Hence the sum=Rs. 15000$