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Question
A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual installments of Rs 500 plus 12% interest on the unpaid amount. How much will be the tractor cost him?
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Solution
value of used tractor = Rs. 12000
cash payment = Rs. 6000
balance = Rs. 12000 – Rs. 6000 = Rs. 6000
payment of an installment = Rs. 500
total installments = `6000/12 = 12`
P Interest on principal at 12% per annum for 1 year = `("p" xx 12 xx 1)/100 = 3/25 "P"`
Payment of amount after one year = 500 + Interest
= `500 + 3/25 xx 6000`
Interest after two years = `3/25` × Rs. 5500 Installment
Payment after 2 years = `(500 + 3/25 xx 5500) "Rs"`
Installment after 12 years = 12 × 500 = 6000
Interest = `3/25 (6000 + 5500 + 5000 + ...... "to 12 terms")`
= `3/25 xx 12/2 [12000 - (12 - 1) xx 500]`
= `3/25 xx 12/2 [12000 - 5500]`
= `3/25 xx 12/2 xx 6500`
= Rs. 4680
Total payment = Rs. (12000 + 4680)
= Rs. 16680
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