Personal Finance and Investing

Fewer discounts –account

Discount Benefit to the buyer

Suppose discount I have to pay you rupees of 2080/ in a year’s time, but you want your money at once. Certainly you cannot demand and I cannot give full rupees of 2080/, what we do then? We find the interest rate prevailing, let us say, is 4%. Clearly I can discharge my debt by paying you rupees 2000/ at once. You lose nothing. Why because if you deposit rupees 2000 / at the prevailing rate, in any bank, it will amount to rupees 2080/ in year’s time.

Now we can easily or understand that rupees 2000/ is the present value (worth), on rupees 2080/ due one year hence. The portion deducted namely, rupees 80/ is the discount.

Definition: The present value or present worth of a sum of money due at the end of a given time is the sum, which with its interest for the given time at the given rate, will amount to the sum due.

The some due is called the amount.

Definition: The true discount is the difference between the sum due at the end of the given time and its present worth.

Thus,

True discount = interest on present worth.

Amount = present worth + discount.

A= P.W+ T.D

P.W = 100 x A                            …………………….. (1)

__________

100 + R x T

Again A = P.W + T.D

= 100 x T.D      + T.D

_________

R x T

100                             R x T + 100

= T.D    [ 1 + _____   ]  =  T.D = [  __________  ]

R + T                            R x T

T.D = A x R x T

__________             ———————————— (2)

Rx T + 100

Present wroth and true discount can be obtained in a much simpler way with the help of formula (1) and (2).

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