Question

A farmer borrows ₹ 1,000 and agrees to repay with a total interest of ₹ 140 in 12 installments. Each installment being less than the preceding installment by ₹ 10. What should be the amount of his first and last installments?

Answer 1

Given: A farmer borrows ₹ 1000 and the paying installments are less than the preceding installment by ₹ 10. Therefore, the given example is an A.P.

Let the first installment be a.

∴ The farmer agrees to repay = 1000 + 140 = ₹ 1140

Here, n = 12, d = –10, S₁₂ = 1140

∴ S_n = `n/2 [2a + (n - 1)d]`

S₁₂ = `12/2[2a + (12 - 1) (-10)]`

1140 = 6[2a + (11)(–10)]

1140 = 6[2a – 110]

`1140/6` = [2a − 110]

190 = [2a − 110]

2a = 190 + 110

2a = 300

a = `300/2`

a = 150

The first installment is ₹ 150.

The last installment (l) is the 12th term (T₁₂) of the AP:

T_n ​= a + (n − 1)d

T₁₂​ = 150 + (12 − 1)(−10)

T₁₂​ = 150 − 110

T₁₂​ = 40

The last installment is ₹ 40.