Question

At what rate per annum will Rs.$640$ amount to $774.40$ in $2$ years, when interest is being compounded annually

Answer 1

Given: $P=$ $640$, $A=$ $774.40$, $n=2$ years, $r=$?

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

$\therefore 774.40=640{(1+\frac{r}{100})}^2$

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

$\frac{77440}{64000}={(1+\frac{r}{100})}^2$

$\frac{121}{100}={(1+\frac{r}{100})}^2$

${\left(\frac{11}{10}\right)}^2={(1+\frac{r}{100})}^2$

$\frac{11}{10}=1+\frac{r}{100}$

$\frac{r}{100}=\frac{11}{10}-1$

$\frac{r}{100}=\frac{11-10}{10}$

$\frac{r}{100}=\frac{1}{10}$

$r=\frac{100}{10}=10$

Rate $r=10$% per annum.