Question

The difference of the compound interest and simple interest on a certain sum money for 3 years at the rate of 10% p.a. is Rs.93. Find the sum.

Answer 1

Let principle amount $=x$

Simple interest $=\frac{P\times R\times T}{100}$

$P=$Principle$=x$

$R=$Rate$=10\%$ Per annum

$T=$Time $=3$ years

$\Rightarrow S.I=\frac{x\times 10\times 3}{100}=\frac{3x}{10}$

Compound interest$=$Amount $-$ Principle

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

$=x{(1=\frac{10}{100})}^3$

$=x{\left(\frac{11}{10}\right)}^3$

$\Rightarrow C.I=\frac{1331x}{1000}-x$

$=\frac{1331x-1000x}{1000}$

$=\frac{331x}{1000}$

Difference of C.I and S.I$=93$

$\Rightarrow \frac{331x}{1000}-\frac{3x}{10}=93$

$\Rightarrow \frac{31x}{1000}=93$

$\Rightarrow x=\frac{93\times 1000}{31}=3000$Rs.

$\Rightarrow$ Sum $=3000$Rs.