Minds On

Savings accounts and credit cards

Money growing over time

Brainstorm

Brainstorm

You want to open a bank account but need to explore the options available to you before heading into the bank. Use the internet to explore the features of both savings and chequing accounts at a few local banks. After a preliminary search, work with a partner, if possible, and brainstorm the following questions:

  • What types of bank accounts are available?
  • What kind of account would you open and what is your personal purpose for the account?
  • What is the difference in interest rate between savings and chequing accounts?
  • What is the purpose of a credit card and why do people use them?
  • What is the interest rate for a typical credit card?

Action

Calculating interest

A savings account is a bank account that pays you interest in exchange for depositing money and maintaining a balance in the account. It is meant to serve as a short-term investment where you deposit some money and earn a little interest on it. Even though the percent of interest earned is small, it is a good way to save up for a big purchase, such as a new electronic device, furniture or a vacation.

For long-term saving goals there are other types of accounts like Registered Savings Accounts such as a Registered Retirement Savings Account (RRSP). They will offer a larger percent of interest, but the intent is that the money is saved over a longer period of time. With a Tax-Free Savings Account (TFSA), you can invest money and not pay any capital gains, but if you lose money, you can't claim a loss.

There are two types of interest applied to savings or loans: simple interest and compound interest.

Simple interest is the percent rate (r) multiplied by the principal amount (P) for a time period (t). This is interest only added on to the original money amount saved or borrowed.

Simple interest can be calculated using the following formula

A = P(1+rt)

Where:

A = final amount

P = principal (initial balance)

r = interest rate (as a decimal)

t = time (the number of years the money is invested)

Compound interest is interest calculated on the amount borrowed plus previous interest. Usually calculated one or more times per year. To calculate: work out the interest for the first period, add it to the total, and then calculate the interest for the next period, and so on. In this case if you are saving, you are making interest on previous interest earned.

Compound interest can be calculated using the following formula

A = P (1+r) t

A = final amount

P = principal (initial balance)

r = interest rate (as a decimal)

t = time (the number of years the money is invested)

Notice how t is an exponent. This makes the amount grow exponentially.

Interest calculation examples

Simple interest example: A gymnast put $500.00 in their savings account for 2 years. They get 2% interest on the principal every 6 months. In this case, it will be four percent because interest is calculated at 6 months, 1 year, 18 months, and 2 years. How much will be in their account after the 2 years?

A = P(1+rt)

A = 500(1+0.02×4)

A = 500(1+0.08)

A = 500(1.08)

A = 540

After 2 years, the gymnast will have $540 in their savings account.

Keep in mind if they keep putting money into the savings, their principal will increase and so will their interest every 6 months. In this case, you would have to calculate compound interest.

Compound interest example: An artist borrowed $200,000.00 to buy a cottage. They got a mortgage rate of 4% compounded annually for 5 years. How much interest will they pay on the amount borrowed? How much will they owe the bank after the 5 years?

A = P (1+r) t

A = 200,000 (1+0.04) 5

A = 200,000 (1.04) 5

A = 200,000 ×1.2166529024

A = 243,330.58

The artist will have to pay back $243,330.58 to the bank. This includes the $200,000.00 they borrowed plus $43,330.58 of interest.

Interest calculation practice

If you would like, you can complete the next word problems using TVO Mathify. You can also use your notebook or the following fillable and printable document.

1. Student A opened a student savings account with the bank. They were having a promotion. If they opened the account there and put a minimum deposit of $1,000, they got a free tablet. They had to keep the money in the account for at least a year. Five years have passed, and Student A realizes that they forgot about the money in the bank account.

Student A knows that the interest rate was supposed to be 3% annually but cannot remember if the interest was simple or compound.

How much money should they have in their account? Calculate both simple and compound interest.

Which do you think they are hoping for, Simple or Compound? Explain.

2. Student B bought a new tracksuit at a sporting goods store. They had a promotion that if they signed up for a credit card and put their purchase on it, they would get a $50 gift card to use for another purchase. Student B signed up for the credit card and put the $108.40 purchase for the tracksuit on the card.

The credit card company has been charging Student B 1.4% interest per month on the credit card for the past 6 months. What is their credit card bill at now? Calculate both simple and compound interest.

Which interest do you think Student B is hoping for on the credit card bill? Explain.

Press the ‘TVO Mathify' button to access to access this resource and the ‘Activity’ button for your note-taking document.

TVO Mathify (Opens in new window) Activity (Open PDF in a new window)

Consolidation

Save or spend

Two friends got $150 each for their birthdays from their grandparents. They both want to buy a new laptop. Friend A is going to put the money in savings and continue to save enough to purchase the laptop outright. Friend B is going to use the $150 towards the laptop purchase and finance the rest using a credit card.

Student standing at an ATM
Student using a laptop

If you would like, you can complete the next word problem using TVO Mathify. You can also use your notebook or the following fillable and printable document.

Friend A decides to put the money in a savings account that gives them 1.5% simple interest per month and save money until they have enough to buy the laptop they want.

Friend B wants to use the $150 right away towards half the purchase of the laptop and put the rest on their credit card and pay it off slowly. The credit card charges 7% compound interest per month on the balance.

Who do you think is making the better choice? Explain your thinking.

Press the ‘TVO Mathify' button to access to access this resource and the ‘Activity’ button for your note-taking document.

TVO Mathify (Opens in new window) Activity (Open PDF in a new window)

Reflection

As you read the following descriptions, select the one that best describes your current understanding of the learning in this activity. Press the corresponding button once you have made your choice.

I feel...

Now, expand on your ideas by recording your thoughts using a voice recorder, speech-to-text, or writing tool.

When you review your notes on this learning activity later, reflect on whether you would select a different description based on your further review of the material in this learning activity.

Discover More

Press ‘Discover More’ to extend your skills.

What is the difference between compound and simple interest? Which one do you prefer? Research a few savings accounts and see what type of interest they use and how often. Research a credit card and a line of credit and see what type of interest they use and how often. Is there a difference when you want to save money and when you want to borrow money? Why do you think this is so?

Connect with a TVO Mathify tutor

Think of TVO Mathify as your own personalized math coach, here to support your learning at home. Press ‘TVO Mathify’ to connect with an Ontario Certified Teacher math tutor of your choice. You will need a TVO Mathify login to access this resource.

Press ‘TVO Mathify’ to join the conversation and connect with a math tutor.

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