Arithmatical - True Discount

CATEGORY

Important facts and Formulae

Suppose a man has to pay Rs. 156 after 4 years and the rate of interest is 14% per annum. Clearly, Rs. 100 at 14% will amount to R. 156 in 4 years. So, the payment of Rs. now will clear off the debt of Rs. 156 due 4 years hence. We say that :

Sum due = Rs. 156 due 4 years hence;

Present Worth (P.W.) = Rs. 100;

True Discount (T.D.) = Rs. (156 - 100) = Rs. 56 =
(Sum due) - (P.W.)

We define : T.D. = Interest on P.W.;Amount = (P.W.) + (T.D.)

Let rate = R% per annum and Time = T years. Then,
1.

P.W. = 100 x Amount / 100 + (R x T) = 100 x T.D / R x T
2.

T.D = (P.W.) x R x T / 100 = Amount x R x T / 100 + (R x T)
3.

Sum = (S.I.) x (T.D.) / (S.I.) - (T.D.)
4.

(S.I.) - (T.D.) = S.I. on T.D.
5.

When the sum is put at compound interest, then
P.W. = Amount / (1 + R /100)T