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A bill of ₹ 4,800 was drawn on 9^{th} March 2006 at 6 months and was discounted on 19^{th} April 2006 for `6 1/4`% p.a. How much does the banker charge and how much does the holder receive?

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#### Solution

Given, Face value = ₹ 4,800,

Date of drawing = 9^{th} March 2006,

Period of the bill = 6 months,

∴ Nominal due date = 9^{th} September 2006,

Legal due date = 12^{th} September 2006,

Date of discount = 19^{th} April 2006

r = `6 1/4 % = 25/4`% p.a.

Now, number of days from the date of discounting to the legal due date:

April | May | June | July | Aug | Sept | Total |

11 | 31 | 30 | 31 | 31 | 12 | 146 |

∴ n = `146/365 = 2/5` year

Since, B.D. = interest on F.V. for n years at r %

i.e., B.D. = `("F.V," xx "n" xx "r")/100`

`= (4800 xx 2/5 xx 25/4)/100`

`= (4800 xx 2 xx 25)/(100 xx 5 xx 4)`

∴ B.D. = ₹ 120

Also, B.D. = F.V. – C.V.

∴ 120 = 4,800 – C.V.

∴ C.V. = 4,800 – 120

∴ C.V. = ₹ 4,680

∴ Banker charges ₹ 120 and holder receives

₹ 4,680.