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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 30th installment? What amount of loan has he paid after 30th installment?
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Solution
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
Tn = a + (n – 1)d
T30 = 1,000 + (30 – 1)100
= 1,000 + 2,900
= 3,900
So, amount paid by him in the 30th installment = ₹ 3,900
and Sn = `"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 30th installment
= 1,18,000 – 73,500
= ₹ 44,500
Hence, he still has to pay ₹ 44500 after 30 installments.
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