Compound interest in Canada: how your money grows over time

If you put $10,000 into an account earning 5% a year, you might expect to earn $500 every year.

That is roughly what would happen with simple interest. Compound interest works differently. Once you earn interest, that interest becomes part of your balance. The next round of interest is calculated on your original money plus the interest you already earned.

Leave the money alone long enough and you begin earning interest on your interest.

For someone saving or investing over decades, that seemingly small difference can become one of the biggest forces behind how much money they eventually accumulate.

A simple example of compound interest

Suppose you deposit $10,000 and earn 5% interest per year.

After the first year:

$10,000 + $500 interest = $10,500

During the second year, the 5% is no longer calculated on $10,000. It is calculated on $10,500.

That produces $525 of interest.

Your balance becomes:

$10,500 + $525 = $11,025

Then the third year's interest is calculated on $11,025.

Nothing dramatic happened in any single year. The important part is that the amount generating the next year's return keeps getting larger.

If the $10,000 remained invested for 10 years at 5%, compounded once a year, it would grow to approximately $16,289.

You deposited $10,000. About $6,289 came from growth.

The compound interest formula in plain English

The standard formula can look intimidating:

Future value = Principal × (1 + rate ÷ compounding frequency)^(compounding frequency × years)

In symbols, you will often see it written as:

A = P(1 + r/n)^(nt)

The letters simply mean:

• A is how much money you end up with.
• P is the amount you start with.
• r is the annual interest rate written as a decimal. A 5% rate is 0.05.
• n is how many times interest is compounded each year.
• t is how many years the money stays there.

For $10,000 earning 5% for 10 years with annual compounding:

$10,000 × (1 + 0.05)^10 = $16,288.95

You do not need to calculate this by hand every time. The formula is useful mainly because it shows the four things controlling the result: how much you start with, your rate of return, how often it compounds and how much time you give it.

When you are ready to test your own numbers, open the full Compound Interest Calculator.

Monthly versus annual compounding

Interest does not always compound once a year.

A financial product might compound:

• annually
• semi-annually
• quarterly
• monthly
• daily

The more frequently interest is added to the balance, the sooner that interest itself can begin earning more interest.

Take the same $10,000, the same 5% annual rate, and the same 10 years.

Monthly compounding leaves you with about $181 more.

There is a difference, but it is worth keeping in perspective. People sometimes spend too much time comparing monthly versus daily compounding when much larger factors are at play.

Your interest rate, how long you save and how much you regularly contribute usually have a far greater effect.

Regular deposits change the picture

Most people do not save for retirement by depositing one amount and never adding another dollar.

They contribute from each paycheque.

Suppose you start with the same $10,000, earn an average 5% annual return compounded monthly and then add $200 at the end of every month.

Over 10 years, you personally contribute:

• $10,000 at the beginning
• $200 × 120 months = $24,000
• Total contributed: $34,000

After 10 years, the account would be worth approximately $47,527.

About $13,527 of the balance comes from growth rather than money you deposited.

Compare that with doing nothing after the original $10,000:

The monthly deposits themselves obviously account for much of the difference. But every early deposit also gets its own opportunity to compound.

The $200 you contribute in month one has almost 10 years to grow. The $200 you contribute in the final month barely has any time at all.

That is why starting earlier can be so powerful even when the monthly amount is modest.

What if you increase the monthly deposit?

Compounding tends to get the attention, but your savings rate is the lever you control most directly.

If you are earning 5%, moving from annual to monthly compounding makes a relatively small difference.

Moving from a $200 monthly contribution to $400 means thousands of additional dollars going to work for you every year.

This is useful when thinking about financial goals. You cannot reliably force an investment to earn 8% instead of 5%. You can often decide to save another $50 or $100 per month.

Compound growth then works on those additional deposits too.

Time makes compound growth look strange

Compound interest does not grow in a straight line.

Imagine $10,000 compounding annually at 5% with no additional deposits.

After five years, it is about $12,763.

After 10 years, about $16,289.

After 20 years, about $26,533.

After 30 years, about $43,219.

The first 10 years produced roughly $6,289 of growth.

Between years 20 and 30 alone, the balance increased by roughly $16,686, even though you never deposited another dollar.

The rate did not change. The account simply had a much larger balance earning that 5%.

This is the part of compounding that becomes difficult to intuit over long periods.

Does compound interest work inside a TFSA or RRSP?

Yes, but a TFSA or RRSP is not itself an investment or interest rate.

Think of accounts such as the Tax-Free Savings Account (TFSA) and Registered Retirement Savings Plan (RRSP) as containers with particular Canadian tax rules.

Inside them, you might hold:

• a savings account
• a Guaranteed Investment Certificate (GIC)
• bonds
• mutual funds
• exchange-traded funds
• stocks

Those assets can generate interest, distributions, dividends or investment growth.

The compounding happens as those returns remain invested and begin producing further returns.

The tax treatment determines how much of that growth you ultimately keep. For example, eligible growth inside a TFSA can compound without Canadian income tax reducing the account along the way.

Compound interest and investment returns are not exactly the same thing

You will often hear people say that stock-market investments benefit from "compound interest."

The general idea is correct, but technically stocks do not usually pay a guaranteed interest rate.

An investment portfolio might gain 8% one year, lose 12% the next and gain 15% after that. Returns fluctuate.

What compounds is the investment return.

If $10,000 grows 10%, you now have $11,000 invested. If the portfolio then rises another 10%, that second gain is $1,100 rather than $1,000 because the first year's gain remained invested.

Compound-interest calculators often assume a constant return such as 5% or 7%. That makes them useful for planning and illustrating scenarios, but an assumed investment return is not a promise of what markets will deliver.

For a savings account or fixed-rate GIC, the calculation can be much more predictable.

Interest rates that look close can produce very different long-term results

A difference of one percentage point can look insignificant when you are choosing between two rates.

Over several decades, it is not.

Higher returns do not simply add a little more money each year. The additional return itself gets compounded again in later years.

The same applies in reverse to fees. If an investment charges a higher fee every year, you lose the fee itself and all the future growth that money could have generated.

That is why small differences become more important as the time horizon gets longer.

Inflation belongs in the calculation too

If a calculator tells you that your savings could grow to $500,000 several decades from now, that does not mean $500,000 will buy what it buys today.

Prices tend to rise over time.

You may therefore see compound-growth projections shown in two ways:

Nominal dollars show the future dollar amount.

Today's dollars, sometimes called inflation-adjusted or real dollars, estimate what that future balance might actually buy compared with today.

Both figures can be useful, but they answer different questions.

The four numbers to pay attention to

For most people using a compound-interest calculator, the calculation comes down to a handful of inputs.

Your starting balance is what is already saved.

Your regular contribution is what you keep adding each month or year.

Your return or interest rate determines how quickly the balance can grow.

Your time horizon determines how long each dollar gets to compound.

Compounding frequency changes the result too, but generally far less dramatically than changing the rate, contribution or number of years.

The lesson from compound interest is therefore less about finding a magical account that compounds more often. It is about getting money invested or earning interest, continuing to add to it, and giving it as much time as possible to grow.