True Discount Important formulas:
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.
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