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Question
Mrs. Gupta repays her total loan of Rs. 1,18,000 by paying installments every month. If the installments for the first month is Rs. 1,000 and it increases by Rs. 100 every month, What amount will she pays as the 30th installments of loan? What amount of loan she still has to pay after the 30th installment?
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Solution
Total amount of loan = Rs. 1,18,000
First installment = a = Rs. 1000
Increase in installment every month = d = Rs. 100
30th installment = t30
= a + 29d
= 1000 + 29 × 100
= 1000 + 2900
= Rs. 3900
Now, amount paid in 30 installments = S30
= `30/2 [2 xx 1000 + 29 xx 100]`
= 15[2000 + 2900]
= 15 × 4900
= Rs. 73,500
∴ Amount of loan to be paid after the 30th installments
= Rs. (1,18,000 – 73,500)
= Rs. 44,500
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