The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

The Simple Discount Formula

We can arrive at a formula for simple discount by thinking back to how we developed the

simple interest formula. We observed that the amount of simple interest should be propor-

tional to the amount borrowed, and that it should also be increased or decreased in proportion

to the loan’s term. From this, we arrived at the simple interest formula:

I  PRT

The same logic applies to discount. If a $500 note is discounted by $20, it stands to reason

that a $5,000 note should be discounted by $200. If a 6-month discount note is discounted by

$80, it stands to reason that a 12-month note would be discounted by $160. Thus, modeling

from what we did for interest, we can arrive at:

FORMULA 2.1

The Simple Discount Formula

D 
 MdT

where

D represents the amount of simple DISCOUNT for a loan,

M represents the MATURITY VALUE

d represents the interest DISCOUNT RATE (expressed as a decimal)

and

T represents the TERM for the loan

The simple discount formula closely mirrors the simple interest formula. The differences

lie in the letters used (D rather than I and d in place of R, so that we do not confuse

discount with interest) and in the fact that the discount is based on maturity value rather

than on principal. Despite these differences, the resemblance between simple interest and

simple discount should be apparent, and it should not be surprising that the mathemati-

cal techniques we used with simple interest can be equally well employed with simple

discount.

Solving Simple Discount Problems

The following examples illustrate the use of the simple discount formula.

Example 2.1.1 A $10,000 face value discount note has a term of 4 months. The

simple discount rate is 6%. Find the amount of the discount.

D  MdT

D  ($10,000)(0.06)(4/12)

D  $200.00

The note would be discounted by $200.

Example 2.1.2 A $5,000 face value note has a term of 219 days. The simple

discount rate is 9^3 ⁄ 8 %. Find the proceeds of the note.

D  MdT

D  ($5,000)(0.09375)(219/365)

D  $281.25

The proceeds can be found by subtracting the discount from the maturity value: $5,000 

$281.25  $4,718.75. Thus the proceeds of the note would be $4,718.75.

With simple interest, we saw that we could use algebra on the formula to find the principal,

the interest rate, or the term. It comes as no surprise that we can do the same sort of thing

with simple discount. The next several examples will demonstrate how the techniques we

developed for simple interest can be applied for simple discount.

2.1 Simple Discount 59