Jaspal Singh repays his total loan of Rs118000 by paying every month starting with the first installment of Rs 1000. If he increases the installment by Rs 100 every month, what amount will be paid by him in the 30th installment? what amount of loan does he still have to pay after the 30th installment?

Given: S_n = Rs 118000

a = Rs 1000

d = Rs 100

To find: S₃₀

Loan after 30^th installment

Formula Used:

Sum of “n” terms of an AP:

Where S_n is the sum of first n terms

n = no of terms

a = first term

d = common difference

Explanation:

Given that,

Jaspal singh takes total loan, S_n = Rs 118000

He repays his total loan by paying every month.

His first installment, a = Rs 1000

Second installment = 1000 + 100 = 1100

Third installment = 1100 + 100 = 1200 and so on

Thus, we have 1000, 1100, 1200, … which form an AP, with

first term, a = 1000

common difference, d = 1100 – 1000 = 100

nth term of an AP

So, amount paid in 30 installments = sum of first 30 terms of this AP

= 15(2000 + 2900)

= 15(4900) = 73500

So, he pays Rs 73500 in 30 installments

Loan left = total loan - paid lone

= 118000 - 73500 = 44500 Rs