Question

A farmer buys a used tractor for Rs. 12000. He pays Rs. 6000 cash and agrees to pay the balance in annual instalments of Rs. 500 plus $12\%$ interest on the unpaid amount. How much will the tractor cost him ?

Answer 1

Total cost of the tractor = Rs. 12000

Cash amount paid = Rs. 6000

Balance amount = Rs. 12000 - Rs. 6000 = Rs. 6000

Interest of 1st instalment

$=Rs.\frac{6000\times 12\times 1}{100}=Rs.720$

Amount of second instalment

$=Rs.\frac{5500\times 12\times 1}{100}=Rs.660$

Amount of second instalment

= Rs. 500 + Rs. 600 = Rs. 1160

Interest of the 3rd instalment

$=\frac{5000\times 12\times 1}{100}=Rs.600$

Amount of third instalment

= 500 + 600 = Rs. 1100

The sequence of instalment is

1220, 1160, 1100 ....

Here a = 1220 d = 1160 - 1220 = -60 and n = 12

$\therefore S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$\therefore S_{12}=\frac{12}{2}[2\times 1220+(12-1)\times -60]$

$=6[2440-660]=Rs.10680$