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A TV set is available for Rs 19650 cash payment or for Rs 3100 cash down payment and 3 equal Yearly installments. If the shopkeeper charges interest at the rate of 10 % per annum compounded as installment plan, calculate the amount of each installment.

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Your problem `->` A TV set is available for Rs 19650 cash payment or for Rs 3100 cash down payment and 3 equal Yearly installments. If the shopkeeper charges interest at the rate of 10 % per annum compounded as installment plan, calculate the amount of each installment.


Cash Price = `19650`

Down Payemnt = `3100`

No of Installment = `3`

Rate = `10`

Remaining Balance = `19650 - 3100 = 16550`

Let Installment = `X`

Now present value of amount of X Rs paid at the end of 1st Year
` = X / ( 1 + 10/100 )`

` = X × 10/11`

Similarly, for `2^(nd)` Year = `X × (10/11)^2`

Similarly, for `3^(rd)` Year = `X × (10/11)^3`

`:.` The total of the present values of the `3` Installment is Rs `( X × 10/11 + X × (10/11)^2 + X × (10/11)^3 )`

and this must be equal to `16550`

`:. ( X × 10/11 + X × (10/11)^2 + X × (10/11)^3 ) = 16550`

`:. X ( 400510/161051 ) = 16550`

`X = 2665394050/400510`

`:.` Installment Amount = `2665394050/400510`

Total Amount Paid `= 2665394050/400510 × 3 = 7996182150/400510`

Interest = Total Paid - Balance Amount `= 7996182150/400510 - 16550 = 1367741650/400510`






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