doing math

courses › Bookkeeping

Invoices & Sales Tax

level 17 course

Bill correctly, add or remove a stated tax, and handle early-payment discounts.

In your head, jot if needed · no calculator why?

Learn first (about 3 minutes)

Opens at level 17.

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the lesson

The idea, the techniques and a tip for each skill, right here. The Learn page adds worked examples for every skill and untimed practice.

Read the lesson · about 3 minutes

The idea

An invoice is the bill you send a customer. Each line is hours times a rate, units times a price, or a flat fee. The lines add up to the subtotal, and any discount comes off that.

Sales tax sits on top, at a stated rate. The tax is a percent of the price before tax, so adding it multiplies the price by 1 plus the rate, and taking it back out divides by that same number.

The tax is not yours. You collect it for the government and owe it until you pay it over, so it is a liability, not revenue.

Techniques

Multiply by 1 plus the rate

Adding a stated sales tax to a price.

  1. Write the rate as a decimal: 8% is 0.08.
  2. The tax is the price times the rate.
  3. The total is the price times (1 plus the rate).
worked example

Example: Assume a sales tax rate of 5%. On a $240 sale, what does the customer pay in total?

  1. Tax: $240 × 0.05 = $12.
  2. Total: $240 + $12 = $252.
  3. In one step: $240 × 1.05 = $252.

Answer: $252

Divide to back out the tax

A total already includes the tax.

  1. The total is the price plus the tax: 110% of the price for a 10% tax.
  2. Divide the total by that share as a decimal, 1.1 here.
  3. Check by adding the tax back on.
worked example

Example: A receipt total of $330 includes an assumed 10% sales tax. What was the price before tax?

  1. The total is 110% of the price.
  2. Price: $330 ÷ 1.1 = $300.
  3. Check: $300 + $300 × 0.1 = $330.

Answer: $300

Early-payment terms

Terms offer a percent off for paying within some days.

  1. Compare the day you pay with the discount window.
  2. Inside the window, take the percent off the invoice.
  3. Outside it, pay the full amount.
worked example

Example: Terms: 2% off if paid within 10 days, otherwise the full amount is due in 30 days. You pay a $1,500 invoice on day 6. How much do you pay?

  1. Day 6 is inside the window.
  2. Pay: $1,500 − $1,500 × 0.02 = $1,470.

Answer: $1,470

Tips by skill

  • TipInvoice total: Multiply hours by the rate and units by the price, add flat fees as written, then take any stated discount off the subtotal.
  • TipAdd sales tax: The tax is the price times the rate. The total is the price times (1 plus the rate). Read which one is asked.
  • TipBack out the tax: Divide the total by 1 plus the rate. Taking the percent off the total gives the wrong price.
  • TipEarly-payment discount: Compare the payment day with the discount window first. Inside it, take the percent off; outside, pay it all.
  • TipSales tax isn't your revenue: Revenue is the sale before tax. The tax collected is owed to the government, so leave it out.

Watch out for

  • Taking the tax percent off a total that already includes tax. The tax was a percent of the smaller price, so divide.
  • Giving only the tax when the question asks what the customer pays in total.
  • Counting sales tax as revenue. It belongs to the government.

skills · practice stats

From rounds of this course only: box, review and test-out answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

  1. 1 day
  2. 3 days
  3. 7 days
  4. 14 days
  5. 30 days
  6. 60 days
  7. mastered · every 90 days

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