Question

Calculate the rate percent when Rs 28000 amount to Rs 30870 in 2 years at compounded annually.

Answer 1

Here P = Rs.28000, A = 30870, t = 2 years

Now, ${\displaystyle \text{P}{(1+\frac{\text{r}}{100})}^{\text{t}}}$ =  A

⇒ ${\displaystyle 28000{(1+\frac{\text{r}}{100})}^2}$

= 30870

⇒ ${\displaystyle {(1+\frac{\text{r}}{100})}^2}$

= ${\displaystyle \frac{30870}{28000}}$

= ${\displaystyle \frac{441}{400}}$

= ${\displaystyle {\left(\frac{21}{20}\right)}^2}$

⇒ ${\displaystyle 1+\frac{\text{r}}{100}=\frac{21}{20}}$

⇒ ${\displaystyle \frac{\text{r}}{100}=\frac{21}{20}-1}$

= ${\displaystyle \frac{1}{20}}$

⇒ R = ${\displaystyle \frac{100}{20}}$

= 5
Hence rate of interest is 5%.