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 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.

TRUE DISCOUNT -> IMPORTANT FORMULAE 

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

Then,

I. P.W. = 100 * Amount / 100 + (R*T) = 100 * T.D. / R * T

II. T.D. = (P.W.)* R * T / 100 = Amount * R * T / 100 + (R * T)

III. Sum = (S.I.) * (T.D.) / (S.I.) - (T.D.)

IV. (S.I.) - (T.D.) = S.I on T.D. V.

When the sum is put at compound interest, then P.W. = Amount / [1+R/100]T;