Question

A man borrowed a sum of money and agrees to pay it off by paying Rs. 43,200 at the end of the first year and Rs. 34,992 at the end of the second year. If the rate of compound interest is 8% per annum, find the sum borrowed.

Answer 1

For the payment of Rs. 43,200 at the end of the first year :
A = Rs. 43200 ; n = 1 year and r = 8 % . To find P.
$A=P_1{(1+\frac{r}{100})}^n\Rightarrow 43200=P_1{(1+\frac{8}{100})}^1$
$\Rightarrow P_1=Rs.43200\times \frac{100}{108}=Rs.40000$
For the payment of Rs. 34,992 at the end of the second year :
$Rs.34922=P_2{(1+\frac{8}{100})}^2$

$\Rightarrow P_2=Rs.34922\times {\left(\frac{100}{108}\right)}^2$

$\Rightarrow P_2=34922\times \frac{100}{108}\times \frac{100}{108}=Rs.30000$
$\therefore$ Sum borrowed = Rs. 40000 + Rs. 30000 = Rs. 70000