Buying Power: The Math Behind Money

Having your own money and being able to make your own purchases is a big step towards becoming an adult. Instead of having to ask your parents for money, you can just think about what you want to buy, figure out if you have enough money, and then buy it. Being in charge of money makes a lot of people anxious - including adults! Buying things and handling money doesn’t have to be complicated, though. You just need to keep math in mind.

Small Purchases

Buying things isn’t that complicated, right? You just hand over your money and you get the thing you paid for. Well, not so fast. There are a couple of things you need to think about.

Let’s say you want to buy a bicycle. You’ve saved up your allowance, or the money you’ve made from a part-time job like a paper route. You go into your local store and see the bike you want. The price tag under it says that it costs $299.99. You have saved up $350, so that’s perfect! You can buy the bike and still have fifty dollars left over to spend how you like, right? Wrong. You still need to pay the sales tax.

Taxes are payments that people make to a government. If you live in Canada, then some of your taxes go to the Government of Canada. Taxes are how the government gets the money they use to do things. They use taxes to build and repair roads, pay for doctors and hospitals, and give people an education.

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Shown is a colour photograph of coins, bills, a tablet and paper with graphs, and children’s wood blocks reading TAX. Shown from above, the objects are piled on a plain black surface, at various angles, like a messy desk. The information in the graphs is too small to read.

There are a lot of taxes you won’t have to deal with just yet. These include income tax and property tax. But you do need to pay sales tax on almost everything you buy in a store. In Canada, they aren’t usually shown on the price tag, either. You have to be able to do some quick math in your head if you want to figure out how much money you need before you get to the cash register.

How much sales tax you’ll pay on your bicycle depends on where you live. In Canada, there are three different types of sales tax. The first is the Goods and Services Tax, or GST. The GST is a federal sales tax. This means that it is the same rate everywhere in Canada. The GST is 5% of the price on the tag. In the case of your bike, that’s 5% of $299.99. We’ll round it up to an even $300 to make it easier. That looks like this:

300 x 0.05 = 15

300 + 15 = 315 

So with the GST added in, you’re actually paying almost $315.

As well as the GST, many provinces have an additional Provincial Sales Tax, or PST. In Quebec this is known as the Quebec Sales Tax, or QST.

For example, in British Columbia and Manitoba the PST is 7% of the purchase price. For your bike, it would look like this:

300 x 0.07 = 21

300 + 21 = 321

So the total, with GST and PST added in, would be:

15 + 21 = 36

300 + 36 = 336

So after taxes, you would have $14 left over from your $350.00

In some provinces, like Ontario and Nova Scotia, the GST and PST are combined into one single sales tax, called the Harmonized Sales Tax, or HST. In Ontario the HST is 13%, and in the Atlantic provinces the HST is 15%.

The sales tax is rarely added to the price on the tag in the store, so it’s important to keep in mind how much extra you’ll need to have to pay.

What if the item you want to buy isn’t in Canada? Let’s suppose that you can’t find a single bicycle you like in Canada. Instead, there’s a bicycle in an online shop based in the United States that is everything you want in a bike. Even better, it’s listed for $269.99. That is thirty dollars cheaper than the bike you would have bought in Canada!

Well, maybe not. Just like sales taxes, the exchange rate is something you need to consider if you’re buying things in or from other countries. The exchange rate determines how much the Canadian Dollar is worth when compared to the currencies of other countries.

At the time of this article, the exchange rate between the Canadian Dollar (CAD) and the U.S. Dollar (USD) is 0.73. This means that each Canadian Dollar is worth 73 cents in the United States, and each U.S. Dollar is worth $1.36 in Canada.

Lower prices in U.S. stores can be deceiving because the Canadian Dollar is worth slightly less. This changes how much you’re actually paying.

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Shown is a colour photograph of two piles of bills, with a calculator on top. Shown from above, colourful Canadian 50, 5, 20, and 10 dollar bills are fanned out on the right. A few black and white American 100 dollar bills are visible on the left. A grey calculator with blue buttons takes up the top left corner of the image. Its screen is not visible.

Let’s take a look at what that would mean for your bike.

In the U.S, the bike you’re looking at is $269.99. The exchange rate between the CAD and the USD is 0.73. This means that each USD is worth 1.36 CAD.

To figure out how much $269.99 USD is in CAD, you have to multiply it by 1.36.

269.99 x 1.36 = 367.19 (rounded up) 

So in your CAD, that $269.99 bike would actually cost you $367.19. That’s more than you’ve saved up!

The exchange rate changes based on the financial market. This means that the value of the Canadian Dollar is based on how much people want to buy and sell it for. It can go up and down based on many different factors. The daily exchange rate between Canada and the United States has hovered around 0.74 for quite a while, but it has gone lower and higher at many points over the last fifty years. When Canadians buy from American stores, they need to keep the exchange rate in mind when thinking about prices.

Larger Purchases

Saving up for a relatively small purchase, like a bicycle, is pretty simple. For larger purchases, like a laptop or a car, it’s a bit more complicated. There are two ways you can go about making a larger purchase. The first is to save up, like you did for the smaller purchase. The second is to use credit.

Saving is likely the way you’ll make this kind of purchase right now. The most common way to save your money is to put it into a bank account. Banks offer many different kinds of accounts. They are usually divided into two types: chequing accounts and savings accounts. Until you have a steady full-time job, you probably won’t need a chequing account. This kind of account is used to store money to use regularly, such as for paying bills.

A savings account allows you to store your money in a safe place until you need to use it. One reason for you to put your money in a savings account is that the bank will pay you interest on it. Interest is the money a bank pays for putting your money into a savings account. How much money depends on the interest rate. The interest rate that a bank pays you differs from bank to bank, and account to account. A typical interest rate for a regular savings account is around 0.01% per day.

Let’s say you saved up $500 from your part-time job and wanted to put it in a savings account. At the end of the first day, how much would you have saved up?

$500 x 0.0001 = $0.05

At the end of that first day you’d have $500.05. To figure out how much you’d make this way over a month, there’s a handy formula:

Interest = Principal x Rate x Time

The Principal is the amount in your savings account. In this case, $500. The Rate is the interest rate, 0.01%. The Time is the period of time you’re saving up for.

One thing to keep in mind with savings accounts, however, are the bank fees. Bank fees are what the bank charges you for their services. Chequing accounts often have a fee that you have to pay monthly in order to have it.

Savings accounts do not typically have this kind of monthly fee. There may be fees for withdrawing money from your account, though, or for transferring money from a savings account to a chequing account.

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Shown is a colour photograph of a parent with two children and their piggy banks at a bank teller’s window. The children are smiling and looking down at two white ceramic pigs on the counter. A bank teller counts a small pile of coins in front of them. The parent is smiling, standing behind the children. Another customer is out of focus in the background.

You get a bank card (often called a debit card) along with your bank account. And you usually have to pay fees for using it. So, when you purchase something using your debit card, you need to remember how much you will need to pay in fees for moving your money, and keep enough aside to cover them.

Until you’re older and you get a full-time job, you probably won’t be able to get credit from a financial institution like a bank or credit union. Credit is money that is given to you as a loan, that you eventually have to pay back with interest. Unlike your savings, the interest on your credit is calculated much more frequently - either monthly or daily.

To see how this works, let’s pretend you owe $2 000 on a credit card. The annual interest rate is 16%. The interest rate is calculated daily, which works out to 0.044% per day. We’ll calculate that for the first few days to show you how it works.

Credit lenders usually require a minimum monthly payment based on your balance at the end of the month. Let’s suppose that minimum payment is 3% of your balance. This would look like this:

2026.40 x 0.03 = 60.79

The minimum payment on your balance would be $60.79. If you pay the minimum payment, your money goes to pay off the interest first. This means that you would pay $26.40 in interest, and $34.39 of the original $2000 balance. This would leave you with a balance of $1965.61.

But how long will it take you to pay back your $2000 balance? If you use a credit calculator, you’ll find out that if you only pay the minimum each month, it will take you 12 years and seven months. Plus you’d pay an extra $1443.76 in interest on top of your original $2000. This would be a total of $3443.76. This is why it’s a good idea to pay more than the minimum payment every month, so you can pay less interest over time.

Handling money is a valuable skill that you can develop at a young age. By understanding the basics of financial math, you can make informed financial decisions that will serve you well in the future. Whether it's managing taxes, dealing with exchange rates, or handling savings and credit, these skills will help you navigate the world of financial math.

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Shown is a colour photograph of two people counting coins at a kitchen table. Coins are spread out on a long wooden table in the foreground. They look like Canadian one and two dollar coins. The young people sit side-by-side, looking down at the table, and sliding the coins with their fingers. In the background are a fridge, stove, and white cupboards.