Question

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

Answer 1

$\bold { \red{EXPLANATION}}$

GIVEN:

C.I−S.I=Rs.283.50

R=15%

n=3 years

TO FIND:

The sum

SOLUTION :

Let the sum be Rs.x

We know that,

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

$A=x(1 + \frac{15}{100})^{3} = x(1.15)^{3} - - - (1)$

Also Simple Interest,

$S.I =\frac{P×R×N}{100} \\ \: \: =\frac{x×15×3}{100} \\ \: \: \: \: \: \: \: \: \: \: = 1.45x - - - (2)$

Thus we have ,

$x(1.15)^{3} −1.45x=283.50 - - (1)and(2)$

$\implies1.523x−1.45x=283.50$

$\implies 0.070875x=283.50$

$\implies x = \frac{283.50}{0.070875}$

$\implies x = 4000$

Thus,

The sum is 4000