Question

A farmer borrowed Rs. $8,000$ and agreed to repay with a total interest of Rs. $1,360$ in $12$-monthly installments, each installment being less than the preceding by Rs. $40$. Find the amount of the first and the last installment.

Answer 1

Farmer borrowed $=$ Rs. $8,000$
Total interest $=$ Rs. $1,360$
Total repayment $=$ Rs. $9,360$
Let first installment be $a,n=12,d=-40,S_n=9,360$
$\therefore S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
$\Rightarrow 9,360=\frac{12}{2}[2a+(12-1\left)\right(-40\left)\right]$
$\Rightarrow 9,360=6[2a-440]$
$\Rightarrow 2a-440=1,560$
$\Rightarrow 2a=1,560+440$
$\therefore a=\frac{2,000}{2}=1,000$
$T_{12}=a+(n-1)d$
$=1,000+11\times -\left(40\right)$
$=1,000-440=560$
$\therefore$ First installment $=$ Rs. $1000$
and last installment $=$ Rs. $560$