##### True Discount

# True Discount Formulas – Quantitative Aptitude

**Important Concepts**

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 R. 156 in 4 years. So, the payment of Rs. 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 Formulae**

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