Discounts and Tax Together

Learn how to calculate the final price when both a discount and sales tax apply to a purchase.

Intermediate25 minLesson
Printable worksheet

Definition

When shopping, you often encounter both discounts (which reduce the price) and sales tax (which increases the price). The key question is: in what order do we apply them?
The Rule: Always apply the discount first, then calculate tax on the discounted price.
Final Price=Original Price×(1−Discount Rate)×(1+Tax Rate)\text{Final Price} = \text{Original Price} \times (1 - \text{Discount Rate}) \times (1 + \text{Tax Rate})
Why this order? Stores are required by law to charge tax only on the amount you actually pay, not on the original sticker price.

Try it now

When a store applies both a discount and sales tax, which should be calculated first?

Worked Examples

A jacket costs 80 dollars and is 25% off. Sales tax is 8%. What is the final price?
1

Calculate the discount amount

80×0.25=2080 \times 0.25 = 20 dollars discount → 20 dollars off
2

Find the discounted price

80−20=6080 - 20 = 60 dollars
3

Calculate tax on discounted price

60×0.08=4.8060 \times 0.08 = 4.80 dollars tax
4

Add tax to get final price

60+4.80=64.8060 + 4.80 = 64.80 dollars

Common Mistakes

Applying tax first, then the discount

Why it's wrong: This incorrectly calculates tax on the full price instead of what you actually pay. It also violates how stores legally must calculate tax.

Correct: Always apply the discount first. Tax is calculated on the sale price, not the original price.

Adding the discount and tax percentages together

Why it's wrong: Thinking '25% off and 8% tax = 17% off total' is wrong because you can't combine these operations.

Correct: Discount and tax must be applied separately in sequence: discount first, then tax on the result.

Forgetting that tax applies to the discounted price

Why it's wrong: Some students calculate the discount correctly but then add tax based on the original price.

Correct: The tax base is always the price you're actually paying after any discounts.

Interactive Visual

Bar Chart

Jacket: 25% off, then 8% tax

Original price(80)
After discount(60)
After tax(64.8)

Interactive Sandbox

Expression Calculator

Try these:

History

No calculations yet

Practice Problems

15 problems
Problem 1 of 15
Easy
When a store applies both a discount and sales tax, which should be calculated first?

Why It Matters

Understanding how discounts and taxes work together is essential for:
  • Smart Shopping: Know exactly how much you'll pay at checkout before you get there
  • Budget Planning: Calculate whether a sale item fits your budget after tax
  • Comparing Deals: Determine which store offers a better final price
  • Avoiding Surprises: No more shock when the total is higher than expected
Every time you see a "25% OFF" sign, you need this skill to know your true cost!

Real World Applications

Black Friday Shopping

During major sales events, stores offer deep discounts. Knowing how to calculate the final price helps you budget.

Example:

A 200 dollar TV is 40% off on Black Friday. With 6% sales tax, the final price is 200×0.60×1.06=127.20200 \times 0.60 \times 1.06 = 127.20 dollars.

1Try It Yourself

You have 100 dollars to spend. A jacket originally costs 120 dollars and is 30% off. Sales tax is 5%.

Can you afford the jacket?

Step 1: Write the mathematical expression

Calculate: 120×0.70×1.05120 \times 0.70 \times 1.05

Online Shopping

E-commerce sites automatically apply discounts and taxes. Understanding the math helps you verify charges.

Example:

A 50 dollar order with a 20% coupon code and 9% tax: 50×0.80×1.09=43.6050 \times 0.80 \times 1.09 = 43.60 dollars.

2Try It Yourself

An online store shows a 90 dollar item with a 15% promo code. Your state has 8% sales tax.

What will you pay at checkout?

Step 1: Write the mathematical expression

Calculate: 90×0.85×1.0890 \times 0.85 \times 1.08

Key Takeaways

  • 1When both discount and tax apply, always calculate discount first, then tax
  • 2Tax is calculated on the discounted price, not the original price
  • 3Use multipliers for faster calculation: (1−discount)×(1+tax)(1 - \text{discount}) \times (1 + \text{tax})
  • 4This order is required by law and reflects what you actually pay

Frequently Asked Questions

By law, stores must charge sales tax only on the amount you actually pay. Since the discount reduces what you pay, tax is calculated on that lower amount.
By law, stores must charge sales tax only on the amount you actually pay. Since the discount reduces what you pay, tax is calculated on that lower amount.
Interestingly, multiplication is commutative, so the final amount is the same either way. However, the legal and practical standard is discount first, then tax. This also makes it clear that you're being taxed on what you actually spend.
Apply all discounts first (usually in the order specified by the store), then calculate tax on the final discounted price.

Glossary

Discount
A reduction in the original price, usually expressed as a percentage (e.g., 25% off)
Sales tax
A government-imposed tax on purchases, calculated as a percentage of the sale price
Multiplier
A decimal used to calculate percent changes in one step (e.g., 0.75 for 25% off)
Sticker price
The original price shown on a product before any discounts
Today's challengeOne problem, three tries

More in This Topic

Introduction to Sales Tax

Elementary20 min

Calculating Tips

Elementary15 min

Understanding Tax Brackets

Advanced25 min

Common Tip Percentages

Elementary15 min