Mark-ups, discounts, GST and interest
What this lesson covers
- Percentages, ratios, rates, and proportions are often applied in financial situations.
You already know how to do all of this
- Mark-up, discount, GST, interest. Four money words.
- There is one piece of maths underneath all four.
- It is the multiplier from last lesson. That is the whole lesson.
Mark-up: what a shop adds on
- A shop pays forty dollars for something. That is the cost price.
- It marks it up 60%, so it multiplies by 1.6.
- Sixty-four dollars on the ticket.
| Step | Working | Note |
|---|---|---|
| Shop pays | $40 | the cost price |
| Marks it up 60% | 40 × 1.6 | |
| Sells at | $64 | the selling price |
Discount: the same move, downwards
- Eighty dollars with 25% off.
- If a quarter comes off, you are paying three quarters of it.
- Times 0.75. Sixty dollars.
| Step | Working | Note |
|---|---|---|
| Ticket price | $80 | |
| 25% off | 80 × 0.75 | you pay 75% of it |
| You pay | $60 |
Both at once, which is the real situation
- The forty-dollar item is on the ticket at sixty-four.
- Now it goes into a sale at 25% off. Forty-eight dollars.
- Still above the forty the shop paid. That is the point of a mark-up.
| Step | Working | Note |
|---|---|---|
| Cost to the shop | $40 | |
| Marked up 60% | $64 | the ticket price |
| 25% off in a sale | 64 × 0.75 | $48 |
| Still above cost | 48 against 40 | the shop is fine |
A question with a surprising answer
- A hundred dollar item goes up 10%. Then it comes down 10%.
- What is the price now?
- It is not a hundred dollars.
Ninety-nine dollars, and here is why
- Up 10% takes a hundred to a hundred and ten.
- Down 10% takes 10% off a hundred and ten, not off a hundred.
- Eleven dollars comes off, not ten. You land on ninety-nine.
| Step | Working | Result |
|---|---|---|
| Start | $100 | |
| Up 10% | 100 × 1.1 | $110 |
| Down 10% | 110 × 0.9 | $99 |
| Not $100 | the 10% off was off a bigger number |
GST, which in New Zealand is 15%
- A price of four hundred and thirty-two dollars before GST.
- The GST itself is 0.15 times that. Sixty-four eighty.
- The price you pay is 432 times 1.15. Four ninety-six eighty.
| Step | Working | Result |
|---|---|---|
| Price before GST | $432 | |
| The GST | 0.15 × 432 | $64.80 |
| Price including GST | 432 × 1.15 | $496.80 |
| Check | 432 + 64.80 | $496.80 |
Now the one that goes the other way
- A receipt says $115, and that price includes GST.
- How much of that $115 is GST?
- Most people take 15% of 115. That is wrong.
Fifteen dollars, not seventeen twenty-five
- 15% of 115 gives $17.25, and it is the wrong answer.
- Something was multiplied by 1.15 to reach 115. So divide.
- 115 over 1.15 is 100. So the GST is 15 dollars exactly.
| Step | What is happening | Value |
|---|---|---|
| A price of $115 including GST | the common wrong answer | 0.15 × 115 = $17.25 |
| What actually happened | × 1.15 landed on 115 | |
| So undo it | 115 ÷ 1.15 | $100 before GST |
| The GST is | 115 − 100 | $15 |
| Check | 100 × 1.15 | $115, correct |
Again, so you can see it is the method
- Two hundred and thirty dollars including GST.
- Divide by 1.15. Two hundred dollars before GST.
- So thirty dollars of GST. Check: 200 times 1.15 is 230.
| Step | Working | Result |
|---|---|---|
| $230 including GST | 230 ÷ 1.15 | $200 before GST |
| The GST | 230 − 200 | $30 |
| Check | 200 × 1.15 | $230, correct |
Simple interest: paid on what you put in
- Two thousand dollars, at 4% a year, for three years.
- Each year pays 4% of the original two thousand. Eighty dollars.
- Three years of that is two hundred and forty.
| Step | Working | Result |
|---|---|---|
| You save | $2000 | the principal |
| At 4% a year | 0.04 × 2000 | $80 each year |
| For 3 years | 80 × 3 | $240 interest |
| You end up with | 2000 + 240 | $2240 |
One honest footnote
- Simple interest always pays on the original amount.
- Real bank accounts pay interest on the interest as well.
- That is compound interest, and it is a later topic.
The claim from the start of the lesson
- Four different words. Look at the middle column.
- Every single one is a multiplier, or undoing one.
- There was never more than one idea here.
| The word | The maths | Direction |
|---|---|---|
| Mark-up of 60% | × 1.6 | a rise |
| Discount of 25% | × 0.75 | a fall |
| Adding GST | × 1.15 | a rise |
| Removing GST | ÷ 1.15 | undoing a rise |
| Simple interest | × rate × years | a rise, once per year |
What to take away
- Six things, and the fourth one will be useful for decades.
| Mark-up and discount | are multipliers, like any percentage change |
| Up then down by 10% | does not return you to the start |
| GST in New Zealand | is 15%, so adding it is × 1.15 |
| GST inside a price | is found by dividing by 1.15, not taking 15% |
| Simple interest | is paid on the original amount every year |
| Every one of these | is the same multiplier idea |
Your turn
- Pause here and try all four.
- Answers are in the description.
| Question | |
|---|---|
| 1 | A shop pays $250 and marks it up 40%. What does it sell for? |
| 2 | A $90 jacket has 30% off. What do you pay? |
| 3 | Find the GST on $60, and the price including GST. |
| 4 | Find the simple interest on $1500 at 5% for 4 years. |
Show answer
1. $350, from 250 × 1.4. 2. $63, from 90 × 0.7. 3. GST is $9, from 0.15 × 60, and the inclusive price is $69. Note this one starts before GST, so you multiply. If it had started at $69 including GST you would divide by 1.15 instead. 4. $300, from 1500 × 0.05 × 4. That is $75 a year for four years.
The answers
- 250 × 1.4, then 90 × 0.7.
- This one starts before GST, so multiply.
- $75 a year, for four years.
| Answer | |
|---|---|
| 1 | $350 |
| 2 | $63 |
| 3 | $9 GST, $69 total |
| 4 | $300 |
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