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A computer is sold by a company for Rs 19200 cash or for Rs 4800 cash down payment together with 5 equal monthly installments. If the rate of interest charged by the company is 12 % per annum, find each installment.

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Your problem `->` A computer is sold by a company for Rs 19200 cash or for Rs 4800 cash down payment together with 5 equal monthly installments. If the rate of interest charged by the company is 12 % per annum, find each installment.


Cash Price = `19200`

Down Payemnt = `4800`

No of Installment = `5`

Rate = `12`

Remaining Balance = `19200 - 4800 = 14400`

At the end of `5` months, Amounts to = `14400 + (14400 × 5 × 12) /(12 × 100) = 14400 + 720`

` = 15120 ->(1)`

Let Installment = `X`

`1^(st)` Installment `= X + (12 × X × 4) / (12 × 100)`

`2^(nd)` Installment `= X + (12 × X × 3) / (12 × 100)`

`3^(rd)` Installment `= X + (12 × X × 2) / (12 × 100)`

`4^(th)` Installment `= X + (12 × X × 1) / (12 × 100)`

Total Installment `= X + ( X + (12 × X × 4) / (12 × 100) ) + ( X + (12 × X × 3) / (12 × 100) ) + ( X + (12 × X × 2) / (12 × 100) ) + ( X + (12 × X × 1) / (12 × 100) )`

Total Installment `= 5 X + (12 × X ×(4 + 3 + 2 + 1))/ (12 × 100)`

Total Installment `= 5 X + 1/10 × X`

Total Installment `= 51/10 X ->(2)`

From (1) and (2)
`51/10 X = 15120`

`X = (15120) / (51/10)`

`X = 50400/17`

`:.` Installment Amount = `50400/17`


`2^(nd)` Method



Cash Price = `19200`

Down Payemnt = `4800`

No of Installment = `5`

Rate = `12`

Remaining Balance = `19200 - 4800 = 14400`

Let Installment = `X`

`:.` Interest Paid = `5 X - 14400 ->(1)`

Principal for `1^(st)` month = `14400`

Principal for `2^(nd)` month = `14400 - 1 X`

Principal for `3^(rd)` month = `14400 - 2 X`

Principal for `4^(th)` month = `14400 - 3 X`

Principal for `5^(th)` month = `14400 - 4 X`

Total `= 72000 - 10 X`

`:.` Interest `= ((72000 - 10 X) × 12 × 1) / (100 × 12) ->(2)`

`:.` From (1) and (2)

`((72000 - 10 X) × 12 × 1) / (100 × 12) = 5 X - 14400`

`(72000 - 10 X) = 500 X - 1440000`

`500 X + 10 X = 72000 + 1440000`

`510 X = 1512000`

`:. X = 50400/17`






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