Formulae on True Discount

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, 1.   P.W. = 100 x Amount = 100 x T.D. 100 + (R x T) R x T 2.   T.D. = (P.W.) x R x T = Amount x R x T 100 100 + (R x T) 3.   Sum = (S.I.) x (T.D.) (S.I.) - (T.D.) 4.   (S.I.) - (T.D.) = S.I. on T.D. 5.   When the sum is put at compound interest, then P.W. = Amount 1 + R T 100