Question

Mohit borrowed a certain sum at $5\%$ per annum compound interest and cleared this loan by paying $Rs.12,600$ at the end of the first year and $Rs.17,640$ at the end of the second year. Find the sum borrowed.

Answer 1

For, $Rs.12,600$, $A=Rs.12,600,r=5\%$ and $n=1$ year.

For, $Rs.17,640$, $A=Rs.17,640,r=5\%$ and $n=2$ years.

Now,

The amount with interest paid at the end of the first year = $Rs.12600$

Using formula,$A=P(1+\frac{r}{100}{)}^n$, where $P$ is the principal at the starting of the first year, we get,

$\Rightarrow 12600=P(1+\frac{5}{100}{)}^1$

$\Rightarrow 12600=\frac{105P}{100}$

$\Rightarrow P=\frac{(12600\times 100)}{105}$

$\Rightarrow P=Rs12000$

Now, the amount of interest paid at the end of the second year = $Rs.17640$

Again using the same formula where principal at the starting of second year is $p$, we get,

$\Rightarrow 17640=p(1+\frac{5}{100}{)}^2$

$\Rightarrow 17640=\frac{105p}{100}$

$\Rightarrow p=\frac{(17640\times 100)}{105}$

$\Rightarrow p=Rs.16800$

$\therefore$ Total sum borrowed = $12000+16800=Rs.28800$