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. [4 MARKS]

Answer 1

Formula : 1 Mark
Application : 1 Mark
Calculation : 2 Marks

Let Rs P be the principal

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

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

$\Rightarrow P=Rs\frac{1600\times 100}{4\times 4}=Rs10000$

Now, we have

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

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

$=Rs10000\times {(1+\frac{10}{100})}^4$

$=Rs10000\times {(1+\frac{1}{10})}^4$

$=Rs10000\times {\left(\frac{11}{10}\right)}^4$

$=Rs10000\times \frac{11}{10}\times \frac{11}{10}\times \frac{11}{10}\times \frac{11}{10}=Rs14641$

$\therefore$ Compound interest = Rs 14641 - Rs 10000 = Rs 4641