Question

A trader paid Rs. 700 to a lender due after 18
months at the rate of 8% for annum simple
interest ? Find present value and true discount.​

Answer 1

Given:

A trader paid Rs. 700 to a lender due after 18 months at the rate of 8% for annum simple interest

To find:

The present value and true discount.​

Solution:

Face value, F.V. = Rs. 700

Time, T = 18 months

Rate of interest, R = 8% per annum S.I.

Finding the present value:

We know,

$\boxed{\bold{F.V. = P.W. \times [1 + \frac{RT}{100} ]}}$

where F.V. = face value, P.W. = present worth, R = rate of interest and T = time

Now, on substituting the values of F.V., R & T in the formula above, we get

$700= P.W. \times [1 + \frac{8 \times \frac{18}{12} }{100} ]}}$

$\implies 700= P.W. \times [1 + \frac{12}{100} ]}}$

$\implies 700= P.W. \times \frac{112 }{100}$

$\implies P.W. = 700 \times \frac{100 }{112}$

$\implies \bold{ P.W. = 625}$

Thus, the present value is → Rs. 625.

Finding the true discount:

We know,

$\boxed{\bold{T.D. = \frac{P.W. \times R \times T}{100 } }}$

where T.D. = True Discount, P.W. = present worth, R = rate of interest and T = time

Now, on substituting the values of P.W., R & T in the formula above, we get

$T.D. = \frac{625 \times 8 \times \frac{18}{12} }{100}$

$\implies T.D. = \frac{625 \times 8 \times \frac{3}{2} }{100}$

$\implies T.D. = \frac{625 \times 12}{100}$

$\implies \bold{T.D. = 75}$

Thus, the true discount is → Rs. 75.

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