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 Rs. 156 in 4 years. So, the payment of
Rs. 100 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,
P.W. = 100 X Amount = 100 X T 100 + (R X T)R X T
T. D. = (P.W.) X R X T = Amount X R X T 100 100 + (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 /