Percentages

New Zealand

Level 5

Lesson

As we've learnt in previous chapters like Sale sale sale! and Money makes the world go round, percentages are very often used when it comes to doing business in our modern world. The hard part in doing the calculations is figuring out what the different business terms mean. Beyond that it's quite easy to find the answer because the calculations are no different to what we've previously done with percentages. Let's define a few terms.

1. **Discount: **how much the cost of something is reduced by. Eg. $10%$10% discount for $\$200$$200 means taking $10%\times\$200=\$20$10%×$200=$20 off the full price of $\$200$$200

2. **Commission: **how much money a salesperson earns. It is usually a percentage of how much they manage to sell. Eg. $50%$50% commission on $\$10$$10 worth of sales is $50%\times\$10=\$5$50%×$10=$5, which is how much the salesperson gets to keep.

3. **Profit: **if an item is sold for more than what it cost to make or obtain, you make a profit. So it is the difference between the selling price and the cost price. Eg. If I bought a bike for $\$10$$10 and sold it for $\$15$$15, my profit is $\$5$$5

4. **Loss: **if an item is sold for less than what it cost to make or obtain, you make a loss. So it is the difference between a product's sale price and buy price when the sale price is lower. Eg. If I bought a bike for $\$20$$20 and sold it for $\$18$$18, my loss is $\$2$$2

5. **Stocks: **a type of 'virtual' product which represents ownership of part of a company

6. **Percentage profit/loss: **the profit/loss as a percentage of the buying price. Eg. I bought a bike for $\$20$$20 and sold it for $\$22$$22, so my percentage profit is $\frac{22-20}{20}\times100%=\frac{2}{20}\times100%$22−2020×100%=220×100% = $10%$10%. A profit of $\$100$$100 sounds good, but is it really that great if the buying price was $\$100000$$100000?

7. **Interest: **if youhave savings in a bank account, or owe money in the form of loans, interest is the amount by which the savings or loans grow. Eg. If I have $\$500$$500 in the bank and the interest rate offered is $10%$10%, I will earn an extra $10%\times\$500=\$50$10%×$500=$50 worth of interest.

A sales assistant is paid a commission of $15%$15% on her weekly sales. Find her commission for a week in which she sells products to the value of $\$2000$$2000.

Luke deposits $\$8635$$8635 in a bank for one year. If the interest rate is $7%$7% p.a:

How much interest, in dollars, did Luke earn for the year? Write your answer to the nearest cent.

Find the total amount (to the nearest cent) in his bank account at the end of the year.

Understand operations on fractions, decimals, percentages, and integers