Question

By using the formula, find the amount and compound interest on:

At what rate per cent per annum will Rs 640 amount to Rs 774.40 in 2 years when compounded annually ?

Answer 1

$\text{Principal (P) = 640}\text{Amount (A) = Rs.774.40}\text{Period (n) = 2 years}\text{Let r be the rate per cent per annum. We know that}A=P{(1+\frac{r}{100})}^n\Rightarrow \frac{A}{P}={(1+\frac{r}{100})}^n\Rightarrow \frac{774.40}{640.00}={(1+\frac{r}{100})}^2\Rightarrow \frac{121}{100}={(1+\frac{r}{100})}^2\text{(Dividing by 64)}\Rightarrow {\left(\frac{11}{10}\right)}^2={(1+\frac{r}{100})}^2\Rightarrow 1+\frac{r}{100}=\frac{11}{10}\Rightarrow \frac{r}{100}=\frac{11}{10}-1=\frac{1}{10}\Rightarrow r=\frac{1}{10}\times 100=10$