Compound Interest Explained: How Your Money Grows on Its Own Growth

Simple interest vs compound interest

With simple interest, you earn interest only on your original deposit, called the principal. With compound interest, the interest you earn is added to your balance, and from then on it earns interest too.

The Ontario Securities Commission's GetSmarterAboutMoney site uses a clear example. Put $100 in an account earning 5% a year. With simple interest, you have $105 after one year, $110 after two and $115 after three. With compound interest, you have $105 after one year, $110.25 after two and $115.76 after three. The difference starts at a few cents because in year two you're also earning 5% on the $5 of interest from year one.

Those cents grow into real money over long periods. Using the same 5% rate, $1,000 earning simple interest for 30 years would grow to $2,500. With annual compounding over the same 30 years, it would grow to about $4,322. Same deposit, same rate, same time; the only difference is that the interest was reinvested.

The examples in this guide use round, hypothetical rates to show how the math works. They are not forecasts, and real returns on investments can be higher, lower or negative in any given year.

The compound interest formula, in plain language

You don't need to memorize a formula to benefit from compounding, but it helps to see what drives it. For a single deposit, the future value is:

• Future value = principal × (1 + rate per period) ^ number of periods

Three things determine the result: how much you start with, the rate you earn per period, and how many periods the money compounds. Of the three, time is usually the one you have the most control over, and because it's an exponent in the formula, it has the most dramatic effect.

Here's an example. $5,000 earning 4% compounded annually grows to about $7,401 after 10 years, about $10,956 after 20 years and about $16,217 after 30 years. Notice that the growth accelerates: the balance rises by about $2,400 in the first decade, about $3,550 in the second and about $5,260 in the third, without a single extra deposit.

If you'd rather not do the math by hand, free tools such as the compound interest calculator on GetSmarterAboutMoney can run the numbers for your own starting amount, contributions, rate and time horizon.

Why compounding frequency matters (a little)

Interest can compound annually, semi-annually, quarterly, monthly or even daily. The more often it compounds, the sooner each bit of interest starts earning interest of its own. Here's what $10,000 at a 5% annual rate becomes after one year at different compounding frequencies:

• Annually: $10,500.00
• Semi-annually: $10,506.25
• Quarterly: $10,509.45
• Monthly: $10,511.62
• Daily: $10,512.67

The difference between annual and daily compounding here is about $13 on $10,000 in a year. It's real, but small. The rate itself and the length of time matter far more than the frequency. When you compare savings accounts or GICs, focus on the rate first, then check how interest is calculated and paid. Our guide to GICs vs high-interest savings accounts explains other differences worth weighing, like access to your money.

Some GICs pay interest out to you annually or at other intervals rather than adding it to the balance. That's simple interest from the account's point of view: unless you reinvest those payments yourself, they don't compound. A compound GIC reinvests the interest automatically and pays it all at maturity.

The rule of 72: a quick way to estimate doubling time

The rule of 72 is a handy mental shortcut. Divide 72 by the annual rate of return, and the result is roughly how many years it takes your money to double. GetSmarterAboutMoney gives the example of a 5% return: 72 ÷ 5 = 14.4, so your money would roughly double in a little over 14 years.

Here's how close the estimate is at different rates, compared with the exact doubling time for annual compounding:

• 2%: rule of 72 says 36 years; the exact figure is about 35 years.
• 4%: rule says 18 years; exact is about 17.7.
• 6%: rule says 12 years; exact is about 11.9.
• 8%: rule says 9 years; exact is about 9.0.
• 10%: rule says 7.2 years; exact is about 7.3.

The rule works best at the kind of rates most savers and investors deal with; it becomes less accurate at very high rates. You can also run it backwards: if you want your money to double in 10 years, you'd need roughly a 7.2% annual return.

The rule of 72 is also a useful warning about debt and inflation. At a 20% interest rate, a debt that's left unpaid doubles in under four years. And if prices rise 3% a year, the purchasing power of cash that earns nothing would be cut roughly in half in about 24 years.

Why starting early matters so much

Because time is an exponent, the years at the start of your saving life are the most valuable ones. A simple comparison shows why. Assume a hypothetical 6% annual return, compounded monthly, and $200 saved every month.

• Alex saves $200 a month from age 25 to 35, then stops completely and leaves the money invested. Total contributed: $24,000. Value at 65: about $197,000.
• Sam waits, then saves $200 a month from age 35 to 65. Total contributed: $72,000. Value at 65: about $201,000.

Sam contributed three times as much money and ended up with roughly the same amount. Alex's first ten years of deposits had 30 extra years to compound. If Alex had kept saving $200 a month from 25 all the way to 65, the total would be about $398,000.

None of this means it's too late if you're starting at 40 or 50. It means the best time to begin is as soon as you reasonably can, even with small amounts, and that increasing your savings later can help make up for a late start. Automating contributions, an approach often called paying yourself first, makes it easier to keep going for long enough for compounding to do its work.

What slows compounding down: fees, taxes and inflation

Compounding works on your net return, after costs. Anything that reduces your return each year also compounds, in the wrong direction.

Fees are the clearest example. $10,000 growing at 6% a year for 30 years becomes about $57,400. If annual fees reduce the return to 4%, the result is about $32,400. A 2-percentage-point difference in annual return cut the final amount by roughly 44%. That's why it's worth knowing what you pay in investment fees, such as a fund's management expense ratio.

Taxes matter too. In a regular non-registered account, interest is generally taxable each year. The CRA notes that interest on a compound GIC must be reported for each complete investment year even though it's paid only at maturity, so you can owe tax on interest you haven't received yet. Holding savings and investments in a TFSA lets growth compound without tax, and an RRSP defers tax until you withdraw.

Finally, inflation erodes what your money can buy. What matters for your long-term goals is your return after inflation. A savings account that pays less than the inflation rate is losing purchasing power, even as its balance grows.

Compounding works against you on debt

When you borrow, compounding is on the lender's side. Unpaid interest gets added to what you owe, and then you pay interest on that interest. High-interest debt such as a credit card balance is where this hurts most.

As a simplified illustration, a $2,000 balance at a 20% annual rate, compounded monthly with no payments or new purchases, would grow to about $2,439 in a year. Real credit card interest is calculated according to your cardholder agreement, often on your daily balance, and our guide on how credit card interest is calculated walks through the details. The direction is the same: the longer a balance sits, the faster it grows.

This is why paying off high-interest debt is often one of the best 'investments' available. Every dollar of a 20% balance you repay saves you that 20% interest, guaranteed, which is hard to match with any savings account or investment.

Putting compound interest to work

You don't need a lot of money or expertise to take advantage of compounding. A few habits do most of the work:

• Start as early as you can, even with small amounts.
• Contribute regularly and automatically.
• Reinvest interest and dividends instead of spending them.
• Keep fees low and use tax-sheltered accounts like a TFSA or RRSP where they fit.
• Pay off high-interest debt, which compounds against you.
• Leave long-term money alone so compounding has time to work.

For short-term goals and emergency savings, safe options like high-interest savings accounts and GICs let your money compound with little risk. For long-term goals, such as retirement decades away, many Canadians invest in diversified portfolios whose value goes up and down but has historically grown over long periods; there are no guarantees. Our guide on how to start investing in Canada is a good next step.

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