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A washing machine is available at Rs 6400 cash or for Rs 1400 cash down payment and 5 monthly installments of Rs 1030 each. Calculate the rate of interest charged under the instalment plan. [ Calculator, Method and examples ]

Solution:
Your problem `->` A washing machine is available at Rs 6400 cash or for Rs 1400 cash down payment and 5 monthly installments of Rs 1030 each. Calculate the rate of interest charged under the instalment plan.


Cash Price = `6400`

Down Payemnt = `1400`

No of Installment = `5`

Installment Amount = `1030`


Remaining Balance = `6400 - 1400 = 5000`

After `5` months Amount = `5000 + 5000 × 5 / 12 × R / 100 = 5000 + (25000 × R) / 1200 `

` = 5000 + 125/6 × R ->(1)`

`1^(st)` Installment = `1030 + (1030 × R × 4) / (12 × 100)`

`2^(nd)` Installment = `1030 + (1030 × R × 3) / (12 × 100)`

`3^(rd)` Installment = `1030 + (1030 × R × 2) / (12 × 100)`

`4^(th)` Installment = `1030 + (1030 × R × 1) / (12 × 100)`


Total Installment `= 1030 × 5 + (1030 × R × (4 + 3 + 2 + 1)) / (12 × 100)`

` = 5150 + (1030 × R × (10)) / 1200`

` = 5150 + 103/12 × R ->(2)`


From (1) and (2)
`5000 + 125/6 × R = 5150 + 103/12 × R`

`125/6 × R - 103/12 × R = 5150 - 5000`

`49/4 × R = 150`


`R = 600/49`

`:. R = 600/49`


`2^(nd)` Method



Cash Price = `6400`

Down Payemnt = `1400`

No of Installment = `5`

Installment Amount = `1030`

Remaining Balance = `6400 - 1400 = 5000`


Total Installment = `1030 × 5 = 5150`

Interest = `5150 - 5000 = 150 ->(1)`

Principal for `1^(st)` month = `5000`

Principal for `2^(nd)` month = `3970`

Principal for `3^(rd)` month = `2940`

Principal for `4^(th)` month = `1910`

Principal for `5^(th)` month = `880`


Total = `14700`

`:.` Installment = `(14700 × R × 1) / (100 × 12) ->(2)`

From (1) and (2)
`(14700 × R × 1) / (100 × 12) = 150`


`R = (150 × 100 × 12) / 14700`

`R = 600/49`






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