TRUE DISCOUNT

Present Worth (P.W.) :-   It is defined as the money gain after the discount on any sum or amount.
    For eg.     If a man borrows Rs 100 at 7 % p.a. simple interest. Then after 2 years, he will have to pay Rs 114.
          or ,     In order to clear off a debt of Rs 114 due 2 years at 7 % p. a. , one has to pay Rs 100 now.
          here,   Rs 100 is called present worth. and,
                     Rs 114 is called amount.

     True Discount (T.D.) = (Amount - P.W.)

    Note :-   Interest is calculated on Present Worth, and
                  True Discount is calculated on amount.

Let Rate = R % p. a.  and Time = T years,  Then

• T.D. = $\frac{P.W.\times R\times T}{100}$  =  $\frac{A\times R\times T}{100+(R\times T)}$

• P.W. = $\frac{100\times Amount}{100+(R\times T)}$  =  $\frac{100\times T.D.}{(R\times T)}$

• Sum = $\frac{(S.I.\times T.D.)}{(S.I.-T.D.)}$

• (S.I.) - (T.D.) = S.I.  on  T.D.