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A bicycle is sold for Rs 1800 cash or for Rs 600 cash down payment followed by 2 monthly installmnets of Rs 610 each. Compute the rate of the interest charged under the installment scheme. [ Calculator, Method and examples ]

Solution:
Your problem `->` A bicycle is sold for Rs 1800 cash or for Rs 600 cash down payment followed by 2 monthly installmnets of Rs 610 each. Compute the rate of the interest charged under the installment scheme.


Cash Price = `1800`

Down Payemnt = `600`

No of Installment = `2`

Installment Amount = `610`


Remaining Balance = `1800 - 600 = 1200`

After `2` months Amount = `1200 + 1200 × 2 / 12 × R / 100 = 1200 + (2400 × R) / 1200 `

` = 1200 + 2 × R ->(1)`

`1^(st)` Installment = `610 + (610 × R × 1) / (12 × 100)`


Total Installment `= 610 × 2 + (610 × R × (1)) / (12 × 100)`

` = 1220 + (610 × R × (1)) / 1200`

` = 1220 + 61/120 × R ->(2)`


From (1) and (2)
`1200 + 2 × R = 1220 + 61/120 × R`

`2 × R - 61/120 × R = 1220 - 1200`

`179/120 × R = 20`


`R = 2400/179`

`:. R = 2400/179`


`2^(nd)` Method



Cash Price = `1800`

Down Payemnt = `600`

No of Installment = `2`

Installment Amount = `610`

Remaining Balance = `1800 - 600 = 1200`


Total Installment = `610 × 2 = 1220`

Interest = `1220 - 1200 = 20 ->(1)`

Principal for `1^(st)` month = `1200`

Principal for `2^(nd)` month = `590`


Total = `1790`

`:.` Installment = `(1790 × R × 1) / (100 × 12) ->(2)`

From (1) and (2)
`(1790 × R × 1) / (100 × 12) = 20`


`R = (20 × 100 × 12) / 1790`

`R = 2400/179`






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