Question

A man repays a loan of ₹ 65,000 by paying ₹ 400 in the first month and then increasing the payment by ₹ 300 every month. How long will it take for him to clear the loan?

Answer 1

Loan Amount = ₹ 65,000

Repayment through installments

400 + 700 + 1000 + 1300 + …

a = 400

d = 300

S_n = 65000

S_n = `"n"/2` (2a + (n – 1)d)

= 65000

`"n"/2` (2 × 400 + (n – 1)300) = 65000

n(800 + 300n – 300) = 130000

n(500 + 300n) = 130000

500n + 300n² = 130000

300n² + 500n = 130000

3n² + 5n – 1300 = 0

(n – 20) (3n + 65) = 0

n = 20, n = `(-65)/3`

∴ n = 20

Number of terms should be (+ ve) and cannot be (– ve) or fractional number.

∴ He will take 20 months to clear the loans.