True Discount

If a person borrows certain money from another person for a certain period and the borrower wants to clear off the debt right now, then for paying back the debt, the borrower gets certain discount which is called True Discount (TD).


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.)

Interest is reckoned on P.W. and true discount is reckoned on the amount.

Now, it is easy for us to define terms like Present Worth (PW), Amount (A) and True Discount (TD).

Present Worth : The money to be paid is called the Present Worth (PW ).

Amount : Sum due is called Amount (A).

Amount (A) = PW + TD

True Discount : It is the difference between the Amount (A) and the Present Worth (PW).

Discount (TD) = A - PW


1. True discount is the interest on Present Worth (PW).

2. Interest is reckoned on PW and TD is reckoned on amount. According to the definition, we have TD = A - PW


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

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

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