Emily asked in Science & MathematicsMathematics · 6 years ago

# Calculate sale discount or tax first?

A warehouse gives a 20% discount on all items, but you also must pay 6% sales tax. Which would you prefer to have calculated first-the discount or the tax? Does it matter?

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• QC
Lv 7
6 years ago

It makes no difference to the customer, although as mentioned by DAC there are rules in most places that requires the discount to be calculated first.

Discount then tax:

Original price = x

Discount: 20% of x = 0.20x

Discounted purchase price before taxes = 0.80x

Sales tax = 6% of 0.80x = 0.06 * 0.80x = 0.048x

Total purchase price = 0.80x + 0.048x = 0.848x

Tax then discount

Original price = x

Sales tax = 6% of x = 0.06x

Purchase price after tax but before discount = x + 0.06x = 1.06x

Discount = 20% on 1.06x = 0.20 * 1.06x = 0.212x

Total purchase price = 1.06x − 0.212x = 0.848

Alternatively:

applying a 20% discount calculated by multiplying by (1−0.20) = 0.80

adding 6% sales tax is calculated by multiplying by (1+0.06) = 1.06

Discount first, then tax = (x * 0.80) * 1.06

Tax first, then discount = (x * 1.06) * 0.80

We can clearly see that both products above will give same result, since multiplication is associative and commutative: (0.80*1.06)x = 0.848x

NOTE: even through neither method makes a difference to the customer, it's better for the retailer if discount is applied first. This is because retailer receives same amount from customer either way, but if tax is calculated first, retailer will have to remit a larger amount in sales tax to the government (0.06x as opposed to 0.048x if discount is applied first)

• 3 years ago

Discount Calculator With Tax

• David
Lv 6
6 years ago

Regardless of what you prefer, most states require that the discount be figured first. The problem, however, asks you to take for example, an item priced at \$1.00, subtract 20%, then add 6%; compare this to adding the 6% first and then subtracting 20% of that total.

• 3 years ago

just fyi- getting the same answer both ways only works if the discount is by percentage. and if there are multiple

items, they all have to be the same percentage off.

it does not work if the discount is a fixed (dollar) amount- like \$50 off all washers or a coupon for \$10 on any pair of boots in the store.

it does not work on a problem with differing percentages- like bogo free (or 50% off), or 2 for 1, or shirts 25% off, pants 40% off and coats 75% off.

it does not work on multiples with fixed amounts- like buy 3 tires, get the 4th one for \$1.

in these cases, it works in the customer's favor to calculate the discount first, then the tax.

:)

• 4 years ago

I dont see where 20% off \$100.00 is the same as 20% off \$106.00. with the tax remaining constant.

The results may be the same but you pay more tax on \$106.00. Who wants to do that to make the equation equal??

• 6 years ago

Calculate it both ways and see what happens.

• 6 years ago

DISCOUNT FIRST

----------------------------

Let the cost be \$100X

20% discount = \$80X

6% tax = \$84.80

TAX FIRST

--------------

Cost = \$ 100X

tax 6% = \$106X

20% discount = \$84.80

THERE IS NO DIFFERENCE

• Michael6 years agoReport

The math is correct but it's incorrect in practice because you gave discount of 20% to the tax. How I wish the IRS would give us discount on Tax!