Question

Find the compound interest at the rate of $10\%$ per annum for four years on the principal which in four years at the rate of $4\%$ per annum gives $Rs.1600$as simple interest.

Answer 1

Let $P$ be the principal.

This principal gives $Rs.1600$ as $S.I.$ in four years at the rate of $4\%$ per annum.

$S.I=\frac{P\times R\times T}{100}$

$\Rightarrow P=\frac{S.I\times 100}{R\times T}$

$\Rightarrow P=\frac{Rs.1600\times 100}{4\times 4}$

$\Rightarrow P=Rs.10000$

Now, we have

$P=Rs.10000,R=10\%$ and $n=4$

$\therefore$ Amount after $4$ years
$A=P{(1+\frac{R}{100})}^n$

$=Rs.10000\times {(1+\frac{10}{100})}^4$

$=Rs.10000\times {(1+\frac{1}{10})}^4$

$=Rs.10000\times {\left(\frac{11}{10}\right)}^4$

$=Rs.10000\times \frac{11}{10}\times \frac{11}{10}\times \frac{11}{10}\times \frac{11}{10}$

$=Rs.14641$

$\therefore$ Compound interest $C.I=A-P$

$=Rs.14641-Rs.10000$

$=Rs.4641$