Question

A small T.V. is available either for full cash payment of Rs.$5000$ or for cash down payment of Rs.$1000$ and five more monthly installments of Rs.$1000$ each. Find the rate of interest.

Answer 1

Let the date of purchase of T.V. be the zero date.

If the person buys on installment basis he pays six months of Rs. $1000$ after $0,1,2,3,4,5$ months.

This is equivalent to paying Rs. $6000$ after a period $D$ from date of purchase, where

$D=\frac{1000\times 0+1000\times 1+1000\times 2+1000\times 3+1000\times 4+1000\times 5}{6000}=\frac{15000}{6000}=2.5$ months

Thus an amount of Rs. $5000$ is equivalent to Rs. $6000$ payable after $2.5$ months.

Let $r\%$ be rate of interest per annum.

Then, $6000=5000[1+\frac{r}{100}\times \frac{2.5}{12}]$

$\Rightarrow \frac{2.5r}{1200}=\frac{6000}{5000}-1$

$\Rightarrow r=\frac{1200}{5\times 2.5}=96$

Thus, the interest is $96\%$ per annum.