Question

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

Answer 1

Principal $=4000$

Compound interest for two years $=Rs410$

$\therefore$ Amount at the end of $2$ years $=A=Rs(4000+410)$

$=Rs.4410$

$\Rightarrow$ Time $2$ years

Let the rate of interest be $r\%$ p.a.

we have,

$\Rightarrow A=P{(1+\frac{r}{100})}^2$

$\Rightarrow 4410=4000{(1+\frac{r}{100})}^2$

$\Rightarrow \frac{441}{400}={(1+\frac{r}{100})}^2$

$\Rightarrow \frac{21\times 21}{20\times 20}={(1+\frac{r}{100})}^2$

$\Rightarrow \sqrt{\frac{21\times 21}{20\times 20}}=\frac{r}{100}+1$

$\Rightarrow \frac{21}{20}-1=\frac{r}{100}$

$\Rightarrow \frac{1}{20}\times 100=r$

$\therefore r=5\%p.a.$

Hence, the answer is $5\%.$