Question

If a certain amount yields interest of rs. 2100 in two years and rs. 3310 in three years, rate of compound interest being the same, what will be the rate of interest?

Answer 1

Therefore the rate of interest will be  57.62%.

Explanation:

Given that a certain amount yields interest of Rs. 2100 in two years and Rs. 3310 in three years and rate of compound interest being same.

Let the principle be x and rate of interest be r.

To find the rate of interest ,we use the following formula

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

A= Amount

P= principle

r= rate of interest

n = time (in year)

According to the problem,

$2100=P(1+ \frac {r}{100})^2$ .........(1)

and  $3310=P(1+ \frac {r}{100})^3$........(2)

Dividing (2) by (1)

$\frac{3310}{2100}=\frac{P(1+\frac{r}{100})^3}{P(1+\frac{r}{100})^2}$

$\Rightarrow \frac{331}{210}= (1+\frac{r}{100})$

$\Rightarrow \frac{r}{100}=\frac{331}{210}-1$

$\Rightarrow \frac{r}{100}=\frac{121}{210}$

⇒r = 57.62

Therefore the rate of interest will be  57.62%.