True Discount
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.
Formulae Used
\[P.W = \frac{100 \times Amount}{100 + \left ( R \times T \right )} = \frac{100 \times T.D }{R \times T } \]
\[T.D = \frac{\left ( P.W \right ) \times R \times T}{100} = \frac{Amount \times R \times T}{100 + \left ( R \times T \right )} \]
\[Sum = \frac{S.I \times T.D}{S.I - T.D} \]
S.I - T.D = S.I on T.D
when the sum is put at compound interest , then
\[P.W = \frac{Amount}{\left ( 1 + \frac{R}{100} \right )^{T}} \]
