Question

At what rate per cent per annum will a sum of $Rs.4000$ yield a compound interest of $Rs.410$ in $2$ years?

Answer 1

Let the rate of interest be $r\%$

Here Principal (P)$=Rs4000$

Time(n)$=2yrs$

$Interest=Rs410$

Now

$Interest=P(1+\frac{r}{100}{)}^2-P\Rightarrow P(1+\frac{r}{100}{)}^2-P=410\Rightarrow P1+\frac{2r}{100}+\frac{r^2}{10000}-1=410\Rightarrow P1+\frac{2r}{100}+\frac{r^2}{10000}-1=410\Rightarrow 4000(\frac{2r}{100}+\frac{r^2}{1000})=410\Rightarrow 400\frac{1}{100}(\frac{r^2}{100}+2r)=410\Rightarrow \frac{r^2+200r}{100}=\frac{410}{40}\Rightarrow r^2+200r=1025\Rightarrow r^2+200r-1025=0\Rightarrow r^2+205r-5r-1025=0\Rightarrow (r+205\left)\right(r-5)=0\therefore r=5Rate=5\%$