Question

The difference between the compound interest and the simple interest on a certain sum of money at $15$% per annum for three years is Rs $283.50$. Find the sum.

Answer 1

Given,

$CI–SI=Rs283.50$

$R=15\%$

$n=3years$

Consider the sum be $RS$$X$

we know that

$\begin{array}{c}A=P{\left(1+\frac{R}{100}\right)}^n\\ =x{\left(1+\frac{5}{100}\right)}^3\\ =x{\left(1.15\right)}^3...\left(1\right)\end{array}$

Also

$\begin{array}{c}SI=\frac{PRT}{100}=\frac{x\left(15\right)\left(3\right)}{100}0.45X\\ A=SI+P=1.45X...\left(2\right)\end{array}$

Thus, we have

$\begin{array}{c}x{\left(1.15\right)}^3-1.45X=283.50\left[From\left(1\right)and\left(2\right)\right]\\ 1.523X-1.45X=283.50\\ 0.070875X=283.50\\ x=\frac{283.50}{0.070875}\\ =4000\end{array}$

Hence, the sum is $RS4000$