How Compound Interest Works: A Plain-English Guide for Canadians
Albert Einstein supposedly called compound interest the eighth wonder of the world. Whether he said it or not, the concept is genuinely powerful — and understanding it is one of the most valuable financial skills you can develop. Here's how it works, with Canadian examples and a free calculator.
Simple Interest vs. Compound Interest
With simple interest, you earn interest only on your original principal. If you invest $10,000 at 5% simple interest for 10 years, you earn $500 per year × 10 = $5,000 total. Your balance after 10 years: $15,000.
With compound interest, you earn interest on your principal plus all previously earned interest. That same $10,000 at 5% compounded annually for 10 years grows to $16,288.95 — an extra $1,288.95 compared to simple interest, just from the compounding effect.
The longer the time horizon, the more dramatic the difference becomes.
The Compound Interest Formula
The formula for compound interest is:
A = P × (1 + r/n)^(nt)
Where: A = final amount, P = principal, r = annual interest rate (as a decimal), n = compounding frequency per year, t = time in years
For example: $10,000 invested at 5% compounded monthly for 10 years:
A = 10,000 × (1 + 0.05/12)^(12×10) = 10,000 × (1.004167)^120 = $16,470.09
Monthly compounding earns more than annual compounding because interest is added to the principal more frequently, and that interest then earns its own interest sooner.
How Compounding Frequency Affects Your Growth
Starting with $10,000 at 5% annually for 10 years, here's how different compounding frequencies compare:
| Compounding Frequency | Final Balance | Total Interest Earned |
|---|---|---|
| Annually (once/year) | $16,288.95 | $6,288.95 |
| Semi-annually (twice/year) | $16,386.16 | $6,386.16 |
| Quarterly (4×/year) | $16,436.19 | $6,436.19 |
| Monthly (12×/year) | $16,470.09 | $6,470.09 |
| Daily (365×/year) | $16,486.65 | $6,486.65 |
The differences seem small over 10 years, but over 30 years they become substantial. More importantly, the interest rate and time horizon matter far more than compounding frequency.
The Rule of 72
A simple mental shortcut: divide 72 by your annual interest rate to find out roughly how many years it takes for your money to double.
- At 4% interest: 72 ÷ 4 = 18 years to double
- At 6% interest: 72 ÷ 6 = 12 years to double
- At 9% interest: 72 ÷ 9 = 8 years to double
This is why starting to invest early makes such a large difference. Money invested at 25 has the potential to double three or four times before retirement, while the same money invested at 45 might only double once.
Compound Interest in Canadian Savings Products
TFSA (Tax-Free Savings Account)
Growth inside a TFSA compounds tax-free. You don't pay tax on the interest, dividends, or capital gains earned within the account — ever. This makes the compounding effect even more powerful because you're not losing a portion of your returns to taxes each year.
RRSP (Registered Retirement Savings Plan)
RRSP growth compounds tax-deferred. You pay tax when you withdraw in retirement — ideally at a lower tax rate than during your working years.
GICs (Guaranteed Investment Certificates)
Canadian GICs typically compound annually or semi-annually. The interest rate is fixed for the term. GICs are low-risk and make the compound interest formula very predictable.
High-Interest Savings Accounts (HISAs)
Most HISAs compound daily and pay interest monthly. The daily compounding on a stated rate means the actual effective rate is slightly higher than advertised.
Calculate Your Compound Interest Growth
See exactly how your savings grow over time with any rate and compounding frequency.
Open Compound Interest Calculator