Question

10. A bill drawn on 5th June for 6 months
was discounted at the rate of 5% p.a. on
19th October. If the cash value of the bill is
Rs 43,500, find face value of the bill.​

Answer 1

Given :-

• A bill drawn on 5th June for 6 months was discounted at the rate of 5% p.a. on 19th October.
• The cash value of the bill is Rs 43,500 .

To Find :-

• Face value of the bill ?

Solution :-

we have given that,

• Date of drawing = 5th June
• Period of the bill = 6 months
• Nominal due date = (5th june + 6 months) = 5th December.
• Legal due date = 8th December . { Date of Bill + Period of Bill + 3 grace Days . }
• Date of discounting = 19th October.
• Cash value (CV) = Rs.43,500 .
• Rate = 5% .

Now,

→ Number of days from the date of discounting to the legal due date = 12(oct.) + 30(Nov.) + 8(Dec.) = 50 days.

we know that,

→ 365 days = 1 year.

So,

→ 50 days = (50/365) = (10/73) years. = Time Period.

we also know that,

• Final value = Cash value + Death benifit.
• FV = CV + DB .
• DB = (final value * Rate * Time) / 100

Putting all values we get,

→ FV = 43500 + [(FV * 5 * 10) / (100 * 73)]

→ FV = 43500 + [FV / 2 * 73]

→ FV = 43500 + (FV/146)

→ FV - (FV/146) = 43500

→ (146FV - FV) / 146 = 43500

→ (145FV/146) = 43500

→ 145FV = 43500 * 146

→ FV = Rs.43,800 (Ans.)

Hence, Face value of the bill is Rs.43,800.

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