Question

What sum of money will amount to Rs. $9,261$ in $3$ years at $5\%$ per annum compound interest?

Answer 1

$A=Rs.9261;n=3$ years and $r=5\%$

$\because A=P{(1+\frac{r}{100})}^n$

$\Rightarrow 9261=P{(1+\frac{5}{100})}^3$

$\Rightarrow 9261=P{\left(\frac{105}{100}\right)}^3$

$\Rightarrow 9261=P{\left(\frac{105÷5}{100÷5}\right)}^3$
$\Rightarrow 9261=P{\left(\frac{21}{20}\right)}^3$

$\Rightarrow P=9261\times {\left(\frac{20}{21}\right)}^3$

$\Rightarrow P=9261\times \frac{20}{21}\times \frac{20}{21}\times \frac{20}{21}$

$\Rightarrow P=9261\times \frac{8000}{9261}$

$\Rightarrow P=Rs.8000$

$\therefore$ Required Sum $=Rs.8000$