Money Bytes · Episode 4 · Money basics · Saving
Simple vs compound interest
Simple interest pays only on the money you started with. Compound interest pays interest on your interest too, so the same money at the same rate can end up more than twice as big.
Simple interest: rent on the first pile only
Interest is the "rent" you earn for letting someone use your money. The amount you start with is called the principal.
With simple interest, the rent is always worked out on that original principal. Put $1,000 away at 10% a year and you earn 10% × $1,000 = $100 every year, no matter how long you wait. After 20 years that's $1,000 + 20 × $100 = $3,000.
Compound interest: interest on interest
With compound interest, each year's interest is added to the balance, and next year's interest is worked out on the new, bigger balance.
- Year 1:
10% × $1,000 = $100, so you have$1,100(the same as simple). - Year 2:
10% × $1,100 = $110, not $100, so you have$1,210. - Year 3:
10% × $1,210 = $121, so you have$1,331.
Each year's interest is a little bigger than the last, because it includes interest earned on earlier interest.
Why time matters so much
The gap starts tiny ($10 after year 2) but keeps growing. The formula for yearly compounding is balance = principal × (1 + rate)^years, so after 20 years: $1,000 × 1.1^20 ≈ $6,727.50. Simple interest ends at $3,000.
Same money, same rate. The only ingredient doing the extra work is time, which is why starting early matters so much for saving.
Try it yourself
Open the SEC's free Compound Interest Calculator on investor.gov. Enter $1,000 as the initial investment, 0 monthly contribution, 20 years, 10% interest, compounded annually, and check that you get about $6,727. Then try a rate closer to what a savings account pays and see how the result changes.
Good to know
- 10% is chosen for easy math, not as a typical or guaranteed return. Savings accounts usually pay much less, and investment returns vary from year to year and can be negative.
- The example assumes compounding once a year and no taxes, fees, deposits or withdrawals.
- More frequent compounding (monthly or daily) grows slightly faster than yearly at the same rate.
- Compounding also works against borrowers: unpaid credit card interest can be charged interest too.
- The math is the same in Canada and anywhere else.
- Educational only, not financial advice.
Why it matters for you
Compound growth rewards patience: the earlier money starts compounding, the more of the final balance comes from interest rather than from what you put in. The next episode gives a quick shortcut, the Rule of 72, for guessing how long it takes money to double.
Test your knowledge
Quick quiz: Simple vs compound interest
4 multiple-choice questions. Pick one answer for each, then check how you did.
Sources
- Investor.gov (SEC), "What is compound interest?": compound interest is interest earned on prior interest as well as the principal
- CFPB, "How does compound interest work?": interest on principal plus accumulated interest; it also applies to debt
- Federal Reserve Bank of St. Louis, "Lesson 6B: Simple and Compound Interest": simple vs compound comparison and the formula V = P(1 + r)^N
- Investor.gov (SEC), "Compound Interest Calculator": checks the $1,000 at 10% for 20 years example
Video transcript
Same money, same rate. One ends up more than twice as big.
Put $1,000 away at 10% a year. With simple interest, you earn rent only on that first thousand: $100, every year.
With compound interest, each year's interest gets added to the pile, and next year you earn interest on the bigger pile. Interest on interest.
Year one, both have $1,100. But in year two, compound earns $110, not $100. The gap keeps growing.
After 20 years, simple interest gives you $3,000. Compound gives you about $6,700. Same money, same rate, just time.
That's your bite. Next: a shortcut to see how fast money doubles.