A bill of Rs. $1800$ drawn on 10th September, $2010$ at $6$ months was discounted for Rs. $1782$ at a bank. If the rate of interest was $5 %$ per annum, on what date was the bill discounted.

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Solution

Banker's Discount (B.D) $=$ Face value $-$ Amount received
$=$ Rs. $1800 =$ Rs. $1782$
$=$ Rs. $18$
Now, B.D is interest on face value for the remaining period
$18 = 1800 \times \frac{5}{100} \times$ Remaining period
Remaining period $= \frac{18 \times 100}{1800 \times 5} = \frac{1}{5}$ year
$\frac{1}{5} \times 365$
$= 73$ days
The bill was drawn on $10^{t h}$ Septmeber, $2010$ for $6$ months so, legal due date is $13^{t h}$ March, $2011$ . This bill was discounted $73$ days before thus counting backwards from 13th March, we have
March $- 13$ days
February $- 28$ days
January $- 31$ days
December $- 1$ day
$∴$ The bill was encashed on $30^{t h}$ December $2010$

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A bill of Rs. 1800 drawn on 10th September, 2010 at 6 months was discounted for Rs. 1782 at a bank. If the rate of interest was 5% per annum, on what date was the bill discounted.

A bill of Rs. $1800$ drawn on 10th September, $2010$ at $6$ months was discounted for Rs. $1782$ at a bank. If the rate of interest was $5 %$ per annum, on what date was the bill discounted.