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A State Government announces sale of flats of Rs 555000 cash or Rs 42750 cash down payment and 3 equal Yearly installments. The Government also charges a nominal interest at the rate of 8 % per annum copuounded as installment plan in this welfare scheme.

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Your problem `->` A State Government announces sale of flats of Rs 555000 cash or Rs 42750 cash down payment and 3 equal Yearly installments. The Government also charges a nominal interest at the rate of 8 % per annum copuounded as installment plan in this welfare scheme.


Cash Price = `555000`

Down Payemnt = `42750`

No of Installment = `3`

Rate = `8`

Remaining Balance = `555000 - 42750 = 512250`

Let Installment = `X`

Now present value of amount of X Rs paid at the end of 1st Year
` = X / ( 1 + 8/100 )`

` = X × 25/27`

Similarly, for `2^(nd)` Year = `X × (25/27)^2`

Similarly, for `3^(rd)` Year = `X × (25/27)^3`

`:.` The total of the present values of the `3` Installment is Rs `( X × 25/27 + X × (25/27)^2 + X × (25/27)^3 )`

and this must be equal to `512250`

`:. ( X × 25/27 + X × (25/27)^2 + X × (25/27)^3 ) = 512250`

`:. X ( 36978525/14348907 ) = 512250`

`X = 7350227610750/36978525`

`:.` Installment Amount = `7350227610750/36978525`

Total Amount Paid `= 7350227610750/36978525 × 3 = 22050682832250/36978525`

Interest = Total Paid - Balance Amount `= 22050682832250/36978525 - 512250 = 3108433401000/36978525`






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