Question

Find the difference between compound interest and simple interest on Rs.$8000$ in $2$ years an at $5\%$ per annum.

Answer 1

We have,

$P=Rs.8000,T=2years,R=5\%$

We know that,

$SI=\frac{P\times R\times T}{100}$

or, $SI=\frac{8000\times 5\times 2}{100}$

or, $SI=Rs.800$

We know that,

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

or, $CI+8000=8000{(1+\frac{5}{100})}^2$

or, $CI+8000=8000{(1+\frac{1}{20})}^2$

or, $CI+8000=8000{\left(\frac{21}{20}\right)}^2$

or, $CI+8000=8820$

or, $CI=Rs.820$

Therefore, the required difference

$CI-SI=820-800$

$=Rs.20$