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True Discount

Suppose a man has to pay Rs. 156 after 4 year 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.

 

Important Formula:

Let rate = R % per annum and Time = T years. Then

  1. True Discount

  2. True Discount

  3. True Discount

  4. (S.I.) – (T.D.) = S.I. on T.D.

  5. When the sum is put at compound interest, then True Discount