Question

At what rate percent annum will $Rs.640$ amount to $Rs.774.40$ in $2$ years, interest being compounds annually?

Answer 1

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

$\Rightarrow 774.40=640{(1+\frac{R}{100})}^2$

$\Rightarrow \frac{77440}{100}=640{(1+\frac{R}{100})}^2$

$\Rightarrow \frac{7744}{10}=640{(1+\frac{R}{100})}^2$

$\Rightarrow \frac{7744}{10}÷640={(1+\frac{R}{100})}^2$

$\Rightarrow \frac{7744}{6400}={(1+\frac{R}{100})}^2$

$\Rightarrow {\left(\frac{88}{80}\right)}^2={(1+\frac{R}{100})}^2$

$\Rightarrow 1+\frac{R}{100}=\frac{88}{80}$

$\Rightarrow \frac{R}{100}=\frac{88}{80}-1$

$\Rightarrow \frac{R}{100}=\frac{88-80}{80}$

$\Rightarrow \frac{R}{100}=\frac{8}{80}$

$\Rightarrow \frac{R}{100}=\frac{8}{80}$

$\Rightarrow \frac{R}{100}=\frac{1}{10}$

$\therefore R=10$

Hence the rate of interest is $10\%$