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Question:
Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?
Answer:

Cost of the scooter = 22000 rupee

Cas payment = 4000

Balance  = 22000 - 4000 = 18000

Now inteset in 1st installment = (18000*10*1)/100 = 1800

Now unpaid amount = 18000 - 1000 = 17000

Again inteset in 2nd installment = (17000*10*1)/100 = 1700

Unpaid amount = 17000-1000 = 16000

Again inteset in 3rd installment = (16000*10*1)/100 = 1600

Unpaid amount = 16000-1000 = 15000

and so on.

Now total ineterst is

 1800, 1700,1600,..........up to 18 terms

It forms an AP

where a = 1800

d = 1700-1800 = -100

n =18

Total ineterst = (18/2)[2*1800 + (18-1)*(-100)]     [Sn =(n/2){2*a + (n-1)*d} ]

                    = 9*[3600 - 1700]

                    = 9*1900

                    = 17100

Now total amount of the scooter = 22000 + 17100 = 39100 rupees  

 

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