The Mathematics of Money

this example is a nationwide chain that has stores in Pennsylvania, it would probably be

required to collect Pennsylvania sales tax on the purchase. If, though, the merchant has no

business operations based in Pennsylvania, it would most likely not collect any sales tax

on this purchase. This does not mean that the purchase is tax-free, only that the merchant

does not collect it. The purchaser may be legally required to pay the tax on the sale to his

state of residence. In those cases, the tax is referred to as a use tax, payable to the state in

which the item purchased is intended to be used.

It will come as no surprise that, in practice, use taxes are often ignored for small pur-

chases, with many people not bothering with, or not even being aware of, their obligation

to pay them. For larger purchases, use taxes generally will be collected, however. One

common example is automobiles, when a car is purchased in one state but registered in

another. Auto dealers often handle the use tax collection for the state in which the vehicle

will be registered.

Calculating Sales Taxes

Sales taxes are normally set as a percent of the amount of the sale. Calculating the sales

tax on a purchase is a matter of converting the percent to a decimal, and multiplying by the

sales amount. The following example will illustrate.

Example 9.1.2 A sweater costs $42.95 and the sales tax rate is 7^3 ⁄ 8 %. Calculate

(a) the amount of sales tax and (b) the total price including tax.

(a) 7^3 ⁄ 8 % is 0.07375 as a decimal. Multiplying this by the price we get (0.07375) ($42.95) 

$3.18.

(b) $42.95 
 $3.18  $46.13

Sales tax is usually calculated this way because the amount of sales tax is usually shown

separately on the receipt. If we are mainly interested in the total, though, we can also

calculate sales tax in a slightly different way. A 7^3 ⁄ 8 % tax rate means that $1 of purchase

price becomes $1.00 
 $0.07375  $1.07375, and so we can just multiply the actual price

by this figure to get the price including tax. We can express this as a formula:

FORMULA 9.1.1

Sales Tax Formula

T 
 P(1  r)

where

T represents the TOTAL PRICE including tax

P represents the PRICE BEFORE TAX

and

r represents the SALES TAX RATE (as a decimal)

Example 9.1.3 Repeat Example 9.1.2, using Formula 9.1.1

Since the formula gives the total price, it is easier to do part (b) fi rst.

T  P(1 
 r)

T  $42.95(1 
 .07375)

T  $42.95(1.07375)

T  $46.13

To answer (a), the amount of sales tax, we can subtract:

$46.13  $42.95  $3.18

If a sale consists of multiple different items, it does not matter (in theory at least) whether

we calculate the tax on each item individually and total the results, or total the items’ prices

first and then calculate the tax on the total.

378 Chapter 9 Taxes