Question

Ranbir borrows Rs. $20,000$ at $12\%$ per annum compound interest. If he repays Rs. $8400$ at the end of the first year and Rs. $9680$ at the end of the second year, find the amount of loan (in Rs.) outstanding at the beginning of the third year.

Answer 1

Given: Principal for the first year $\left(P\right)=Rs.20,000,r=12$%
We know that $A=P{(1+\frac{r}{100})}^n$
Amount after the first year $=20,000{(1+\frac{12}{100})}^1$
$=20,000\left(\frac{112}{100}\right)$
$=Rs.22,400$
Money repays at the end of first year $=Rs.8,400$ (given)
Principal for the second year $=Rs.22,400-Rs.8,400$
$=Rs.14,000$
Amount after second year $=14,000{(1+\frac{12}{100})}^1$
$=Rs.15,680$
$\therefore$ The loan outstanding at the beginning of the third year
$=Rs.15,680-Rs.9,680$
$=Rs.6,000$