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?
Confused about this question, can anyone help?
- QCLv 76 years agoFavorite Answer
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
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)
- DavidLv 66 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.
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- 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??
- Who, me?Lv 76 years ago
Calculate it both ways and see what happens.
- ranjankarLv 76 years ago
Let the cost be $100X
20% discount = $80X
6% tax = $84.80
Cost = $ 100X
tax 6% = $106X
20% discount = $84.80
THERE IS NO DIFFERENCE