Rounding Discounts and Sales Tax

Date: 03/20/2002 at 20:01:12
From: Nilla Salgueiro
Subject: Rounding discounts and sales tax

I wonder why the math book that I teach from states the following:  
When computing sales tax always round up before adding on to the 
price. Ex: 14.9305 rounds to 14.94. When computing discounts always 
round down before subtracting from the original price. Ex: 3.9975 
round to 3.99.  

This seems confusing to the students. Why can't you follow rounding 
rules?

Date: 03/20/2002 at 23:26:28
From: Doctor Twe
Subject: Re: Rounding discounts and sales tax

Hi Nilla - thanks for writing to Dr. Math.

In most states, businesses are free to round taxes (and discounts) any 
way they want to. The State simply computes the sales tax the business 
owes the State based on total gross sales - not on actual "sales tax 
collected."

Most businesses, however, round as your book suggests so that the 
business never gets "shortchanged." In fact, they are likely to "over 
collect," and they keep the difference. As a simple example, suppose 
we have a 5% sales tax and 100 people come in and buy a $.48 item. 
Using the "conventional" rounding rules, each of the 100 customers 
would be charged a sales tax of:

     $.48 * 5% = $.48 * .05 = $.024 --> $.02

For 100 customers, that totals:

     100 * $.02 = $2.00

The State, however, sees gross sales of:

    100 * $.48 = $48.00

and charges the company:

   $48.00 * 5% = $48.00 * .05 = $2.40

So the company has to pay the state $2.40 but only collected $2.00 in 
sales tax. The company loses $.40 in the process.

On the other hand, using your book's rounding rules, if 100 people 
come in and buy a $.48 item, each of these customers would be charged 
a sales tax of:

     $.48 * 5% = $.48 * .05 = $.024 --> $.03

For 100 customers, that totals:

     100 * $.03 = $3.00

The State still sees gross sales of:

    100 * $.48 = $48.00

and charges the company:

   $48.00 * 5% = $48.00 * .05 = $2.40

This time, the company *gains* $.60 instead!

Similar logic applies to the discount situation; rounding down always 
gives the company the extra fractional cent, assuring that they're 
not "shortchanged."

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/