Question

Mr. Sharma borrowed a certain sum of money at $10\%$ per annum compounded annually. If by paying Rs. $19,360$ at the end of the second year and Rs. $31,944$ at the end of the third year he clears the debt; find the sum borrowed by him.

Answer 1

Let the term borrowed by Mr. Sharma $=x$

At the end of $2$ years, the amount at the rate of $10\%$ be $A_1$

Hence, amount $A_1=P(1+\frac{r}{100}{)}^2$

$A_1=x{(1+\frac{10}{100})}^2$

Then he pays back $Rs19360$

So for the third year, the principal amount is $A_1-19360$

He cleared the debt by paying $Rs.31944$ at the end of the third year.

$\Rightarrow A_2=P(1+\frac{r}{100}{)}^n$

$\Rightarrow 31944=(P(1+\frac{10}{100}{)}^2-19360)\times (1+\frac{11}{100}{)}^1$

$\Rightarrow 29040=(P(1+\frac{10}{100}{)}^2-19360)$

$\Rightarrow P(1+\frac{10}{100}{)}^2=48400$

$\Rightarrow$ Sum borrowed $=40000Rs$