Tax, Tips, and Simple Interest

By the end of this lesson you will be able to:

• Identify the base in any percent problem
• Compute tax, tip, markup, markdown, commission, and fees
• Calculate simple interest using

What You Will Learn Today

By the end of this lesson, you will be able to:

1. Identify the type of percent problem and the base the percent is applied to
2. Solve problems involving tax, tip, markup, markdown, commission, and fees
3. Calculate simple interest using and solve for any variable

Percent Problems Start with One Equation

Every percent context is one equation: part = rate × whole

One Equation Covers All Percent Contexts

Always Identify the Base First

The BASE is the quantity the percent is applied to.

• Tax → base: purchase price (before tax)
• Tip → base: meal cost (before tip)
• Commission → base: total sales
• Markdown → base: original price

Ask before computing: "Percent of WHAT?"

Worked Example 1: Sales Tax

A book costs $14.99. Sales tax is 7%. What is the total cost?

Step 1: Convert the rate:

Two-step method:

• Tax
• Total

One-step method:

• Total ✓

Worked Example 2: Markdown Then Tax

Shoes: $85, 30% off, 6% sales tax. Final price?

Step 1: Sale price

Step 2: Tax

Step 3: Total

Tax base = $59.50 (discounted price), not $85 (original)

Check: Tax on Original or Sale Price?

A $120 jacket is on sale for 35% off. The tax rate is 9%.

What is the correct base for the tax computation?

A) $120 (original price)
B) $78 (sale price after 35% off)

What is the final price?

Answer: Tax Base Is the Sale Price

Base for tax = $78 (discounted price)

• Sale price
• Total ✓

Wrong: → total (tax on original price)

Worked Example 3: Markup and Commission

Wholesale: $18,000, markup 22%, commission 4% on selling price.

Step 1: Selling price

Step 2: Commission

Commission base = selling price, not wholesale cost

Percent Contexts: Add or Subtract?

Add (percent increases the total): tax, tip, markup, fee, commission
Subtract (percent reduces the total): markdown, discount

One-step shortcut:

• Add: multiply by (e.g., for 7% tax)
• Subtract: multiply by (e.g., for 35% off)

Practice: Find Tax, Tip, and Total

A meal costs $28.50. Tax is 8.5%. Tip is 20% on the pre-tax amount.

Find: (a) tax amount, (b) tip amount, (c) total bill

Set up: Tax base = _____ | Tip base = _____

Practice Answer: Tax and Tip Computed

Tax base = $28.50 | Tip base = $28.50

• Tax:
• Tip:
• Total:

Shortcut check: Post-tax price , then ✓

Transition: Percent Growing Over Time

You know how to find what percent does to a quantity right now.

What if the percent accumulates over YEARS?

A bank account earns 3% interest per year. How does your money grow?

This brings us to simple interest — percent applied to money over time.

Introducing the Simple Interest Formula

Worked Example: Finding Interest and Total

$800 at 5% annual interest for 3 years. Find and .

Check: ✓ | (not just )

Rearranging the Formula for Each Variable

Any of the four variables can be the unknown — rearrange before substituting.

Worked Example: Solving for Time

How long to earn $120 in interest at 4% on $1,000?

Worked Example: Finding the Rate

$600 earns $54 in interest over 3 years. What is the annual rate?

Convert your answer back to percent:

Check: Find the Starting Principal

A savings account earns $90 in interest over 2 years at 4.5% annually.

What was the principal deposited?

Set up the rearranged formula before substituting.

Answer: Principal Was One Thousand Dollars

Check: ✓

Always verify: plug your answer back into and confirm the interest matches.

Practice: Convert Months Then Calculate Interest

A loan of $2,400 at 3% annual interest for 18 months. How much interest is paid?

Step 1: Convert time to years:

Step 2: Apply

Summary: Percent of a Quantity and Interest

• part = rate × whole — identify the base first
• Add (): tax, tip | Subtract (): discount
• ; — rate decimal, time years

Wrong base | not | vs.

What's Next: Percent Change and Error

Deck 1 covered: percent of a quantity (tax, tip, markup, markdown, commission) and simple interest

Deck 2 will cover:

• Percent increase and percent decrease
• Chain of percent changes (and why +20% then −20% ≠ 0%)
• Percent error in measurement contexts
• Multistep synthesis problems