# DISCOUNT

, or Rebate, is used for an allowance made on a bill, or any other debt not yet become due, in consideration of making present payment of the bill or debt.

Among merchants and traders, it is usual to allow a sum for discount that is equal to the interest of the debt, calculated for the time till it becomes due: but this is not just; for as the true value of the discount is equal to the difference between the debt and its present worth, it is equal only to the interest of that present worth, instead of the interest on the whole debt. And therefore the rule for finding the true discount is this:

As the amount of 100l, for the given rate and time:

Is to the given sum or debt::

So is the interest of 100l, for the given rate and time:

To the discount of the debt.

So that, if p be the principal or debt, r the rate of interest per cent. and t the time; then as , which is the true discount. Hence also is the present worth, or sum to be received.

For ex. Suppose it be required to find the discount of 250l, for five months, at the rate of 5 per cent. per annum interest. Here p=250, r=5, and t = 5/12 or 5 months; then the discount sought.

A Table of Discounts may be seen in Smart's Tables of Interest, the use of which makes calculations of discount very easy.

Discount is also the name of a rule in books of Arithmetic, by which calculations of Discount are made.

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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