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 /
(1 +
^{R}/_{100})^{T}