F. Financial Literacy · Money and Finances: Exchange Rates, Budgets, Financial Decisions and Interest

How Interest Rates Affect Savings and Investments

F1.5 A1About 45 minutes

Learning goals

I can calculate interest earned on savings year by year.
I can explain how interest earns interest over time.
I can explain how a higher interest rate or a longer time changes savings.
I can compare savings and investments, including risk and inflation.

Words to know

principal
The amount of money you first save, invest or borrow.

interest rate
Interest as a percent of the principal, usually per year.

compound interest
Interest that is added to your balance and then earns interest itself: interest on interest.

investment
Something you put money into hoping it grows, like a GIC, a bond, stocks or a mutual fund.

GIC
Guaranteed Investment Certificate: you agree to leave money in for a set time and get a set, guaranteed rate.

risk
The chance that an investment could lose value or grow less than you hoped.

return
How much an investment earns or loses.

Remember from Grade 6

In Grade 6 you learned that an interest rate is a percent, usually per year. You found the interest for one year: $500 at 3% earns $15. You learned that a higher rate is good when you save and bad when you borrow, and that fees matter too.

In Grade 7 you'll see what happens over many years. Time turns small differences into big ones.

Two cousins, one gift

Aisha and Ben each get $1000 from their grandparents to save for after high school.

Aisha puts hers in an account that pays 2% a year.
Ben puts his in a GIC that pays 6% a year (both are example rates).

They don't add or take out any money. After 5 years, who has more? How much more? It's more than you might think.

Interest on interest

In most savings accounts and GICs, the interest you earn is added to your balance. The next year, you earn interest on the new, bigger balance, including last year's interest. This is called compound interest.

To find each year's balance:

Interest = rate × balance at the start of the year.
New balance = old balance + interest.
Repeat for each year.

A calculator or spreadsheet makes this quick. In Grade 8 you'll explore this growth more with digital tools.

Year	Aisha: 2% a year	Ben: 6% a year
0 (start)	$1000.00	$1000.00
1	$1020.00	$1060.00
2	$1040.40	$1123.60
3	$1061.21	$1191.02
4	$1082.43	$1262.48
5	$1104.08	$1338.23

Balances at the end of each year, rounded to the cent. Example rates.

Ben's balance at 6% a year, labels rounded to the dollar. The bars grow a little more each year because interest earns interest. (Bars start at $0.)

Worked example

Example 1: Ben's first two years

Ben has $1000 at 6% a year. Find his balance after 1 year and 2 years.

Year 1: 6% of 1000 = 0.06 × 1000 = $60. Balance: 1000 + 60 = $1060.
Year 2: 6% of 1060 = 0.06 × 1060 = $63.60. Balance: 1060 + 63.60 = $1123.60.
Year 2's interest ($63.60) is more than year 1's ($60). The extra $3.60 is interest on last year's $60 of interest.

$1060 after 1 year and $1123.60 after 2 years.

Worked example

Example 2: How much does the rate matter?

Use the table. After 5 years, how much more does Ben have than Aisha? How much interest did each earn?

Aisha's interest: 1104.08 − 1000 = $104.08.
Ben's interest: 1338.23 − 1000 = $338.23.
Difference: 1338.23 − 1104.08 = $234.15.

Ben has $234.15 more. His rate is 3 times Aisha's, and he earned more than 3 times as much interest ($338.23 vs $104.08), because interest on interest grows faster at a higher rate.

Worked example

Example 3: Interest on interest vs. interest only on the principal

If Ben's GIC paid 6% only on the original $1000 each year (not on the interest), how much would he have after 5 years? Compare.

Each year: 6% of 1000 = $60.
5 years: 5 × 60 = $300 interest. Balance $1300.
With interest on interest: $1338.23. Difference: $38.23.

Interest on interest added $38.23 in 5 years. Over 20 or 30 years, the difference gets much bigger. That's why starting to save early helps.

Both bars start with $1000 and add 5 × $60 = $300. When interest also earns interest, an extra $38.23 grows on top.

Worked example

Example 4: Savings vs. inflation

Aisha's $1000 earns 2% in one year. Prices rise 3% that year (example). Did her purchasing power go up or down?

Her money: 1000 + 20 = $1020.
Things that cost $1000 now cost 1000 + 30 = $1030.

Her purchasing power went down a little: $1020 buys less than $1000 did a year ago. To grow purchasing power, savings need to earn more than the inflation rate.

Savings and investments: rate vs. risk

Savings accounts: you can take money out any time. Usually a low rate. Very low risk.
GICs: a guaranteed rate, often higher than a savings account, but you agree to leave the money in for a set term (like 1 to 5 years). Low risk.
Stocks (small pieces of ownership in a company) and mutual funds (a mix of many investments): no guaranteed rate. Over long periods they may grow more, but their value can go down too, sometimes a lot. Higher risk.

In general, investments that might earn more usually come with more risk. Grown-ups often talk with a qualified advisor and choose a mix that fits their goals and how long they can wait.

Time is your friend

Two things make savings grow more: a higher rate and more time. You can't control interest rates, but you can control when you start. Even small amounts saved early can grow a lot.

Use a calculator, show your steps

Year-by-year interest is lots of steps. Use a calculator, and write each year's balance in a table so you (or a partner) can check every line. Rounding to the cent each year is fine; your answers may differ by a cent from someone who didn't round.

Just for fun

Compound interest is like a snowball rolling down a hill: the bigger it gets, the more snow it picks up on each roll.

Hands-on activity

Grow your money table

You need: paper and a pencil, a calculator (or a spreadsheet with a grown-up).

Choose a starting amount, like $500.
Make a table with columns: Year, Balance at 1%, Balance at 4%, Balance at 8%.
Fill in 10 years. For each year, multiply the balance by the rate to find the interest, then add it.

Shortcut: multiplying by 1.04 does both steps for 4% at once (because 1.04 = 1 + 0.04).

Draw a bar graph or line graph of the three accounts.
Write two sentences about what you notice. When does the 8% account pass $1000?

What to look for: each year built from the year before, correct rounding to the cent, and an observation like "The gap gets bigger every year." (At 8%, $500 first passes $1000 in year 10: $1079.46, after $999.50 in year 9.)

Your turn

$400 is saved at 3% a year. How much interest in the first year? What is the balance?

Continue: what is the balance after year 2?

$2000 at 5% for 2 years with interest on interest. Find the balance.

Which grows more in 5 years: $1000 at 2% or $1000 at 6%? Use the table.

What is the difference between a savings account and a GIC?

Your savings earn 1% and inflation is 2%. Does your money's purchasing power go up or down?

Why do stocks have more risk than a GIC?

More practice: warm-up

10% of $300 = ?

$300 at 10% for 1 year. Balance?

What is principal?

$1000 at 4% for 1 year. Interest?

Higher interest rate on savings: good or bad for the saver?

More practice: on your own

$800 at 5% for 3 years with interest on interest. Find each year's balance.

Same $800 at 5%, but interest only on the original $800. Balance after 3 years? How much less than with interest on interest?

Sophie saves $1000 in a GIC at 4% for 2 years. Liam saves $1000 in a savings account at 1.5% for 2 years. How much more does Sophie have?

Savings of $600 earn 3% in a year. Inflation is 2%. Did purchasing power go up or down? By about how many dollars' worth?

Why might a grown-up choose a savings account even though a GIC pays more?

Challenge

Jamie puts $1000 at 6% at age 13. Ella puts the same $1000 at 6%, but starts 2 years later. When Jamie is 18, Jamie has saved for 5 years and Ella for only 3. Using the table, how much more does Jamie have then?

A stock fund grows +12% one year and −10% the next. A GIC grows +2% each year. Starting with $1000, which has more after 2 years?

About how many years does it take $1000 at 6% to grow past $1300? Past $1400?

Check your understanding

Quiz

$500 earns 4% a year. What is the balance after 1 year?

$1000 at 10% for 2 years with interest on interest gives...

What is compound interest?

Which two things make savings grow more?

Which investment has a guaranteed rate?

Savings earn 2%; inflation is 4%. What happens to purchasing power?

For parents and teachers

Big idea: F1.5 asks students to explain how interest rates can impact savings, investments, and the cost of borrowing to pay for goods and services over time. This lesson covers savings and investments; the next covers borrowing. Students calculate interest year by year to see the effect of rate and time. (Formal simple and compound interest with digital tools is a Grade 8 expectation, so we keep the method step by step here.)

Common difficulties:

Using the original amount every year when interest is compounding. Each year starts from the new balance.
Percent of a decimal, like 6% of 1123.60. A calculator is fine; check the size of the answer.
Thinking investments always grow. Stocks and funds can go down.
Forgetting inflation when judging whether savings really "grew".

How to help: Build the Grow your money table on a spreadsheet together. If your child has a savings account, look at the interest it earned. All rates are examples and not advice. This lesson builds A1 skills: perseverance with multi-step calculations and using tools strategically.