Question

A bill is drawn for Rs.7000 on
3rd May for 3 months and is discounted on 25th May at 5.5%. Find the present worth.

Give the answer if you know it

don't give any other​

Answer 1

Given:

A bill is drawn for Rs.7000 on  3rd May for 3 months and is discounted on 25th May at 5.5%.

To find:

The present worth.

Solution:

Amount, A = Rs. 7000

The rate of interest, R = 5.5%

We are given that,

• The bill is drawn on 3rd May

• After 3 months, the nominal due date is 3rd Aug and the legal due date will be on 6th of Aug

• The bill is discounted on 25th May

∴ The remaining period (T) will be,

= [6 days of May] + [30 days in June] + [31 days in July] + [6 days of Aug]

= 6 + 30 + 31 + 6

= 73 days

= $\frac{73}{365} \:year$

= $\frac{1}{5} \: year$

∴ The true discount (T.D.) is,

= $\frac{A\times R\times T}{100 + (R\times T)}$

= $\frac{7000\:\times\:5.5\:\times\:\frac{1}{5} }{100 \:+\: (5.5\:\times\:\frac{1}{5})}$

= $\frac{7000\:\times\:1.1}{100\:+\:1.1}$

= $\frac{7700}{101.1}$

= $76.1622$

Now,

The present worth (P.W.) of the bill is,

= $\frac{100\: \times \:T.D.}{R\: \times\: T}$

= $\frac{100\: \times \:76.1622}{5.5\: \times\: \frac{1}{5} }$

= $\frac{7616.22}{1.1}$

= $\bold{6923.83}$

Thus, the present worth of the bill is Rs. 6923.83.

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