Question

A farmer borrowed $Rs.60,000$ and agreed to repay with interest in a year in twelve monthly installments. The first installments was $Rs.12,000$. the next each installment was less than the preceding one by $Rs.1000$. Find the total amount he paid in the whole year and what was the interest charged?

Answer 1

Total amount $=Rs.60000$

First installment $\left(a\right)=Rs.12000$

Common difference $\left(d\right)=-Rs.1000$

Total no. of months in which amount to be paid $\left(n\right)=12$

Therefore,

Total amount paid by farmer

$=\frac{n}{2}[2a+(n-1)d]=\frac{12}{2}[2\times 12000+(12-1)(-1000\left)\right]=6\times (24000-11000)=6\times 13000=Rs.78000$

Interest paid by farmer $=78000-60000=Rs.18000$