Question

The difference between CI and SI on a certain sum for $2$ years at $7.5\%$ p.a. is Rs. $360$. Find the sum.

Answer 1

compound interest - simple interest=$360$ rupees

$T=2years$

$R=7.5\%P.a$

$\left(i\right)C.I=P{\left[1+\frac{R}{100}\right]}^T$

$\left(ii\right)S.I=\frac{P\times R\times T}{100}$

$C.I-I.S=P{\left[1+\frac{R}{100}\right]}^T-\frac{R\times T}{100}$

$360=P{\left[1+\frac{7.5}{100}\right]}^2-\frac{7.5\times 2}{100}$

$360=P{\left[\frac{4.3}{4}\right]}^2-\frac{15}{100}$

$360=P\left[1.155-\frac{15}{100}\right]$

$360=P\left[1.155-0.15\right]$

$36P\left(1\right)$

$\therefore P=360Rupees$