# True Discount Formulas

IMPORTANT CONCEPTSSuppose 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 FORMULAELet rate = R% per annum and Time = T years. Then,

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