Grade by Grade
B. Exponential Functions · Financial Mathematics: Compound Interest and Annuities

Making Saving, Investing and Borrowing Decisions in Canada

B3.6 B3.7 B3.2About 75 minutes
Learning goals
  • I can use compound interest and annuity calculations to compare real saving, investing and borrowing options.
  • I can read current Canadian rates and rules, note their date and source, and use them in calculations.
  • I can weigh things the formulas do not show: risk, access to money, fees and rules.
  • I can make and justify a financial decision, and say what would change my mind.

Words to know

policy interest rate
The Bank of Canada's target for the overnight rate. Banks' own rates (such as prime) tend to move with it.
prime rate
A bank's base lending rate. Lines of credit and variable-rate loans are often priced as "prime + some %".
grace period (credit card)
The time between the statement date and the due date during which new purchases are interest-free if the full balance is paid.
deposit insurance
Protection of eligible deposits if a member institution fails. CDIC covers up to $100 000 per eligible category at each member institution.
liquidity
How quickly and easily you can get your money without a penalty.
risk
The chance that an investment loses value or earns less than expected.

Math meets real life

You now have a complete toolkit: A = P(1 + i)ⁿ and its present value, the rate and the time, and the future value, present value and payment of annuities. In this lesson you will use the whole toolkit on decisions Canadians really make: where to keep savings, how to pay for something big, and what borrowing really costs. You will also use real, dated Canadian rates and rules. Because rates change, every real number below says when it was true and where it comes from.

1. GoalWhat, how much,by when?2. Optionssave, investor borrow?3. CalculateFV, PV, payment,total interest4. Beyond mathrisk, access,fees, rules5. Decideand explainwhyA five-step decision processIf the result is not affordable or too risky, go back to step 2 and change a condition.
Good financial decisions use the math (step 3) and the things the formulas leave out (step 4): risk, how fast you can get your money, fees, and the rules.

The Canadian rate landscape (checked October 16, 2026)

  • Bank of Canada policy rate: 2.25%. The Bank held its target for the overnight rate at 2.25% on September 2, 2026 (Bank Rate 2.5%, deposit rate 2.20%). It has been 2.25% since the Bank lowered it on October 29, 2025. The next scheduled decision is October 28, 2026. Source: Bank of Canada press releases, bankofcanada.ca.
  • Prime rate at the big banks: 4.45% in October 2026. Source: Ratehub.ca prime rate page, updated October 16, 2026. Many lines of credit charge prime plus a margin.
  • Credit cards: federally regulated institutions must give a minimum 21-day interest-free grace period on new purchases if you pay the full balance by the due date (it does not apply to cash advances or balance transfers). The FCAC's example rates are 19% on purchases and 22% on cash advances. Source: Financial Consumer Agency of Canada, "How credit cards work", modified October 15, 2025.
  • Criminal interest rate: 35% APR. Since January 1, 2025, the Criminal Code makes it a crime to charge more than 35% APR on most loans (it was 60% effective annual rate before). Source: Canada Gazette, Part II, June 19, 2024.
Some Canadian interest rates and limits (checked October 2026)Bank of Canada policy rateheld Sept 2, 20262.25%Prime rate, big banksOct 20264.45%FCAC example: card purchasesFCAC page, Oct 202519%FCAC example: cash advancesFCAC page, Oct 202522%Criminal interest rate (APR)since Jan 1, 202535%0%5%10%15%20%25%30%35%40%Annual rate. Rates change: check the source before any real decision.
The FCAC's example credit card purchase rate (19%) is more than four times the big banks' prime rate (4.45%). The bars show rates as stated by each source at the dates given; they are not offers.

Rules that protect savers (checked October 2026)

  • TFSA: for Canadian residents 18 and older. The 2026 dollar limit is $7 000 (the same as 2024 and 2025); someone who has been eligible since TFSAs began in 2009 and never contributed has $109 000 of room in 2026. Growth and withdrawals are tax-free. Source: Canada Revenue Agency limit as reported by Harvest Portfolios and Questrade, 2026.
  • CDIC deposit insurance: eligible deposits, including GICs, at a CDIC member institution are protected up to $100 000 per eligible category, per member institution (for example, savings in your name and savings in a TFSA are separate categories). Source: cdic.ca. Investments such as stocks and mutual funds are not covered.
  • Student loans: the Canada Student Loans and Canada Apprentice Loans portions have been interest-free since April 1, 2023. Source: Employment and Social Development Canada news release, March 2023. Provincial portions have their own rules; check ontario.ca/osap.
Worked example

Example 1: Four ways to pay for a laptop

Riya needs a $1 500 laptop for college. Compare: (a) save first, depositing at the end of each month for 12 months at 2.4% compounded monthly (an example savings rate), then buy; (b) pay cash now from savings; (c) borrow on a line of credit at 6.45% (prime 4.45% + 2%) compounded monthly, repaid over 12 months; (d) put it on a credit card at 19.99% compounded monthly and repay over 12 months.

  1. (a) Saving goal: R = 1500 × 0.002 ÷ [(1.002)¹² − 1] ≈ $123.63 per month. Deposits: 12 × 123.63 = $1 483.56; interest supplies about $16.44.
  2. (b) Cash: $1 500 now, but her emergency savings shrink.
  3. (c) Line of credit: R = 1500 × (0.0645 ÷ 12) ÷ [1 − (1 + 0.0645 ÷ 12)⁻¹²] ≈ $129.41. Total ≈ 12 × 129.41 = $1 552.92; interest ≈ $52.92.
  4. (d) Credit card: R = 1500 × (0.1999 ÷ 12) ÷ [1 − (1 + 0.1999 ÷ 12)⁻¹²] ≈ $138.94. Total ≈ $1 667.28; interest ≈ $167.28.

If she can wait, saving first is cheapest. If she needs it now, the line of credit costs about $114 less than the credit card. The credit card would cost nothing extra only if she paid the full balance within the grace period.

Total paid for a $1 500 laptop over 12 monthsSave first, then buy$1 483.56deposits; interest pays $16.44Pay cash now$1 500.00no interest; savings dropLine of credit, 6.45%$1 552.92interest $52.92Credit card, 19.99%$1 667.28interest $167.28$1 400$1 500$1 600$1 700Out-of-pocket total. The axis starts at $1 400, not $0.
The four options from Example 1. Waiting and saving costs the least; borrowing at a credit card rate costs the most. Math shows the cost, but the decision also depends on how urgently Riya needs the laptop.
Worked example

Example 2: Paying only a little on a card

Owen owes $3 000 on a credit card at 19.99% compounded monthly. Compare paying it off in 24 months with moving it to a line of credit at 6.45% compounded monthly and paying it off in 24 months. (Assume no new purchases and no fees.)

  1. Card: R = 3000 × (0.1999 ÷ 12) ÷ [1 − (1 + 0.1999 ÷ 12)⁻²⁴] ≈ $152.67. Interest ≈ 24 × 152.67 − 3000 = $664.08.
  2. Line of credit: R ≈ $133.57. Interest ≈ 24 × 133.57 − 3000 = $205.68.
  3. Difference: about $458 in interest, and $19.10 a month less.

Moving the balance to the lower rate saves about $458. (Real balance transfers may have fees; read the agreement. The best plan is to avoid carrying a balance at all.)

Worked example

Example 3: Where should a TFSA deposit go?

Elena, 18, will put $7 000 (the 2026 TFSA limit) into her TFSA. Option A: a 5-year GIC at an example rate of 3% compounded annually, CDIC-insured, locked in. Option B: a high-interest savings account (HISA) at an example rate of 2.25% compounded monthly, insured, withdraw any time. Option C: a stock index fund, which has no guaranteed rate and can lose value. Compare A and B after 5 years and discuss C.

  1. A: 7000(1.03)⁵ ≈ $8 114.92.
  2. B (if the rate stayed the same, which is not guaranteed): 7000(1 + 0.0225 ÷ 12)⁶⁰ ≈ $7 832.68.
  3. A earns about $282 more, but the money is locked in for 5 years. B can be withdrawn for an emergency.
  4. C cannot be calculated with A = P(1 + i)ⁿ, because the rate is not fixed. Over long periods stocks have often grown faster than GICs, but their value can fall, sometimes for years.

There is no single right answer. Money needed within a few years usually belongs in insured, low-risk options (A or B); money for goals many years away might accept more risk (C). A good answer uses the numbers and explains the trade-off between return, risk and access.

Just for fun

A bank teller offers you a pen chained to the counter, and a GIC that locks your money in for five years. Both are secured for your protection.

Hands-on activity

Rate detective

You need: a phone or computer, paper, a calculator. Work with a parent or guardian; never enter personal information on any website.

  1. Look up today's Bank of Canada policy rate (bankofcanada.ca) and write it with the date.
  2. On the public website of a Canadian bank or credit union, find: a savings account rate, a 1-year GIC rate, a line of credit or personal loan rate (often shown as prime + %), and a credit card purchase rate. Write each with the date and the source.
  3. Calculate: (a) what $1 000 would grow to in 1 year in the savings account and in the GIC; (b) the monthly payment and total interest on a $2 000 loan repaid over 2 years at the loan rate and at the credit card rate.
  4. Write a short recommendation for a friend who wants to buy a $2 000 used e-bike. Include at least one thing the numbers do not show.

What to look for: every rate has a date and a source; correct i and n; a recommendation that mentions both cost and something like risk, access to money, or the grace period on credit cards.

Your turn

1

The policy rate is 2.25% and prime is 4.45% (October 2026). A line of credit is offered at prime + 3%. What is its rate?

2

A $1 000 purchase is charged to a credit card and the full balance is paid by the due date, within the grace period. How much interest is charged on that purchase?

3

Find the monthly payment and total interest on a $1 000 credit card balance at 19.99% compounded monthly, repaid over 3 years with no new purchases.

4

Is a loan at 39% APR legal in Canada in 2026 under the Criminal Code? Explain.

5

Mila saves $150 at the end of each month for 2 years. Compare the FV at 2.5% and at 3.5% compounded monthly.

6

Name two things, other than the interest rate, to consider before choosing a GIC instead of a savings account.

More practice: warm-up

1

What is the 2026 TFSA dollar limit, and what is the minimum age to open a TFSA?

2

Up to how much does CDIC protect per eligible category at a member institution?

3

Since what date have Canada Student Loans been interest-free?

4

Which usually has the higher interest rate: a credit card or a line of credit?

5

Why should every real rate you write down include a date?

More practice: on your own

1

Riya (Example 1) can wait 6 months instead of 12. What monthly deposit at 2.4% compounded monthly reaches $1 500 in 6 months?

2

A store offers "$0 down, $65 a month for 24 months" on a $1 400 TV. Find the total paid. What annual rate (compounded monthly) does this hide? Use a TVM Solver or guess and check with PV = 65[1 − (1 + i)⁻²⁴] ÷ i.

3

Elena (Example 3) chooses the HISA. After 2 years she needs $1 000 for a car repair. Why is that easier with the HISA than with the GIC?

4

A $5 000 personal loan is offered at 9.5% compounded monthly over 3 years. Another lender offers 8.5% over 4 years. Compare payments and total interest.

5

Explain why the Bank of Canada's policy rate matters to someone with a variable-rate line of credit.

Challenge

1

Elena puts $7 000 into her TFSA at the end of each year for 5 years in a GIC ladder averaging 3% compounded annually. Find the FV. Then explain why CDIC coverage matters for her total.

2

Payday-style loan: borrow $300 and repay $345 two weeks later. Treat this as one compounding period of 2 weeks. What is i per period? What is the APR (i × 26)? Compare with the 35% APR criminal rate.

3

Write a recommendation for Owen (Example 2): should he move his $3 000 balance to the line of credit? Include the math, one risk, and one habit change.

Check your understanding

Quiz

1.

As of October 2026, the Bank of Canada's policy interest rate is:

2.

Which option for a $1 500 purchase costs the least, if you can wait?

3.

Since January 1, 2025, Canada's criminal interest rate is:

4.

A credit card purchase is paid in full by the due date. The interest charged on it is:

5.

Which is NOT covered by CDIC deposit insurance?

6.

A 5-year locked-in GIC usually pays more than a savings account because:

7.

Why should a financial decision include more than the calculation?

For parents and teachers

Big ideas (B3.6, B3.7, B3.2): Students apply compound interest and annuity calculations to real Canadian choices about saving, investing and borrowing, investigate how conditions change the result, and justify a decision. All real figures are dated and sourced:

  • Bank of Canada policy rate 2.25%, held September 2, 2026 (bankofcanada.ca); next decision October 28, 2026.
  • Big-bank prime rate 4.45% (Ratehub.ca, October 16, 2026).
  • Credit card 21-day minimum grace period and example rates of 19% and 22% (Financial Consumer Agency of Canada, page modified October 15, 2025).
  • Criminal interest rate 35% APR from January 1, 2025 (Canada Gazette, Part II, June 19, 2024).
  • TFSA 2026 limit $7 000 and cumulative room $109 000 (CRA, as reported by financial institutions, 2026).
  • CDIC coverage up to $100 000 per eligible category per member institution (cdic.ca).
  • Canada Student Loans interest-free since April 1, 2023 (ESDC, March 2023).

These numbers change, so please check the sources before relying on them. The savings and loan rates in the examples (2.4%, 3%, 6.45%) are illustrations, not offers.

How to help: Do the Rate detective activity together. Share (at a comfort level that suits your family) how you decided on a loan, a mortgage or where to keep savings. Emphasize two habits: pay credit cards in full within the grace period, and start saving early, even small amounts.

Common difficulties: using an annual rate as a monthly rate; forgetting that a lower payment over a longer term can cost more; ignoring risk and access to money.