Question

A certain sum of money invested at the rate of 10 percent per annum compounded annually, the interest for the first year plus the interest for the third year is Rs. 2,652. Find the sum.

Answer 1

Let the sum of money=$Rs.x$

Rate $=10$ per annum

$Amount=P{(1+\frac{R}{100})}^n$

For the first year

$Amount=x(1+\frac{10}{100})=\frac{11}{10}x$

$Interest=\frac{11}{10}x-x=\frac{1}{10}x$

For the second year

$P=Rs.\frac{11}{10}x$

$Amount=\frac{11}{10}x(1+\frac{10}{100})=\frac{121}{100}x$

For the third year

$P=Rs.\frac{121}{100}x$

$Amount=\frac{121}{100}(1+\frac{10}{100})=\frac{1331}{1000}x$

$Interest=\frac{1331}{1000}x-\frac{121}{100}x=\frac{121}{1000}x$

According to the question

The interest for the first year plus interest for the third year=Rs.2652

$\Rightarrow \frac{1}{10}x+\frac{121}{1000}x=2652$

$\Rightarrow 0.221x=2652$

$\Rightarrow x=\frac{2652}{0.221}$

$\Rightarrow x=12000$