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).
For example: If a person has to pay ₹ 160 after 4 yr and the rate of interest is 15% per annum. It is clear that ₹ 100 at 15% will amount to ₹ 160 in 4 yr. Therefore, the payment of ₹ 100 now will clear off the debt of ₹ 160 due 4 yr hence at 15% per annum.
Thus, following points are outcomes
1. Sum due is equal to ₹ 160 due 4 yr hence.
2. Present Worth (PW) is ₹ 100.
3. True Discount (TD) = ₹ (160 - 100 ) = ₹ 60 = (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
MIND IT !
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,|