Quantitative Aptitude :: True Discount

Present Value: The present worth of the money is important to understand before settling into the true discount. Any money that is to be paid before the due date is cleared off for debt is known as the present worth of the money.

True Discount: True discount can be understood in reference to this present worth. The difference between the present worth of the money and the amount is known as the true discount.
True discount = (amount - present worth)

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 + (R x T)} = ^{100 x T.D.} ⁄_{R x T}

2. T.D. = ^{(P.W.) x R x T}⁄₁₀₀= ^{Amount x R x T}⁄_{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}