Question

At what rate per cent per annum willl $Rs640$ amount to $Rs774.40$ in $2$ years, interest being compound annually?

Answer 1

Since, interest is compounded anvally

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

$794.40=640{(1+\frac{R}{100})}^2$

$\Rightarrow {(1+\frac{R}{100})}^2=\frac{774.40}{640}=\frac{7744}{6400}$

$\Rightarrow 1+\frac{R}{100}=\frac{\sqrt{7744}}{\sqrt{6400}}=\frac{88}{80}$

$\Rightarrow 1+\frac{R}{100}=\frac{110}{100}$

$\Rightarrow \frac{R}{100}=\frac{110-100}{100}$

$\Rightarrow R=10$

$\therefore$ Rate is $10\%$ per annum.