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 Present Worth; Amount = Present Worth + True Discount
Interest is reckoned on P.W. and true discount is reckoned on the amount.
Let rate = R% per annum and Time = T years. Then,
P.W. = (100 x Amount) / (100 + (R x T)) = (100 x T.D.)/ (R x T)
T.D. = (P.W. x R x T) / 100 = (Amount x R x T) / (100 + (R x T))
Sum = (S.I. x T.D.) / (S.I. - T.D.)
S.I. - T.D. = S.I. on T.D.
When the sum is put at compound interest, then P.W. = Amount/ (1+R/100)T