Question

Rohan repays his total loan of ₹ 1,18,000 by paying every month starting with the first installment of ₹ 1,000. If he increases the installment by ₹ 100 every month, what amount will be paid by him in the 30^th installment? What amount of loan has he paid after 30^th installment?

Answer 1

Total loan = ₹ 1,18,000

First installment = ₹ 1000

Since, he increases the installment by ₹ 100 every month.

∴ Monthly installments paid by Rohan are 1000, 1100, 1200, 1300, ............ 30 terms

∴ a = 1,000, d = 100, n = 30

T_n = a + (n – 1)d

T₃₀ = 1,000 + (30 – 1)100

= 1,000 + 2,900

= 3,900

So, amount paid by him in the 30^th installment = ₹ 3,900

and S_n = `"n"/2[2"a" + ("n" - 1)"d"]`

S₃₀ = `30/2[2 xx 1,000 + (30 - 1)100]`

= 15[2,000 + 2,900]

= 15 × 4900

S₃₀ = 73,500

So, total amount paid by Rohan in 30 installments = ₹ 73,500

Therefore amount left after the 30^th installment

= 1,18,000 – 73,500

= ₹ 44,500

Hence, he still has to pay ₹ 44500 after 30 installments.