Compound Interest

Compound interest is interest earned on an amount that already includes earlier interest. Each period, the interest is added to the balance, and the next period's interest is worked out on the larger figure. The formula is A = P(1 + r/n)^(nt). Three things drive the result: the rate, the time, and how often interest is credited. Projections built on it overstate it in three ways, which you will learn to spot below.

The arithmetic is honest. What goes into it is where the trouble starts. Learn both halves and you can read any projection put in front of you, from a savings offer, a loan, a pension statement or an insurance illustration, and see what it really says.

What is compound interest?

Interest earned on the principal and on the interest already added to it.

Simple interest is paid only on the original amount, so every year produces the same figure. Compound interest is paid on a balance that grows, so every year produces a little more than the one before at the same rate. Two years are enough to see it. Illustrative example: $1,000 earning 5% a year becomes $1,050 after one year. Leave the $50 in place and the second year earns $52.50, not $50, so the balance ends at $1,102.50. The extra $2.50 is interest on interest.

That extra looks trivial in year two. It is not trivial in year thirty, because by then, in the example below, most of the balance is interest that has been earning interest for decades. The same mechanism works on debt: when unpaid interest is added to a balance that itself carries interest, the debt compounds too. The arithmetic does not care which side of the table you sit on.

How do you calculate compound interest?

The formula is A = P(1 + r/n)^(nt), and each letter has one job.

• P is the principal, the amount you start with.
• r is the yearly rate written as a decimal, so 6% is 0.06.
• n is the number of times interest is credited each year: 1 for yearly, 2 for half-yearly, 12 for monthly, 365 for daily.
• t is the number of years.
• A is the total at the end, principal included. Subtract P to see the interest alone.

The bracket, 1 + r/n, is the growth in one crediting period. The exponent, n times t, is the number of periods. Multiply the starting amount by the one-period growth, as many times as there are periods, and you have the result.

Keep its limits in mind. This version describes a single lump sum left alone at a steady rate. It does not include later deposits, withdrawals, tax, fees or inflation. Each of those has its own step, and each is covered further down. If a number is quoted to you without saying which of them it includes, it includes none of them.

What does the formula give on real numbers?

Illustrative example. Take $10,000 at 6% a year, credited once a year, left alone for up to thirty years. These are round inputs chosen for the arithmetic, not a rate anyone is offering and not a projection of any product.

For ten years: P is 10,000, r is 0.06, n is 1 and t is 10. The bracket is 1.06, the exponent is 10, and 1.06 to the tenth power is about 1.7908. So A is about $17,908, of which about $7,908 is interest. Simple interest on the same terms would be $600 a year, or $6,000. The difference of about $1,908 is compounding.

The table carries the same example forward, and adds one column a projection can leave out: what the balance would buy in today's dollars if prices rise 3% a year, an assumed inflation rate chosen for illustration.

Read the last row slowly. Compounding turns $10,000 into about $57,435, far more than the $28,000 simple interest would give. That is real. But in today's purchasing power the $57,435 is worth about $23,662, before any tax on the growth and before any fee. The arithmetic did not change between the third and fourth columns. Only the honesty of the presentation did. To convert any future figure yourself, divide it by (1 + inflation) raised to the number of years.

How much does compounding frequency change the result?

Less than advertising suggests, and it is still worth understanding, because it is how two quoted rates become comparable.

When interest is credited more than once a year, each credit starts earning sooner, so the same nominal rate produces a slightly higher effective annual rate. The formula is: effective annual rate = (1 + r/n)^n minus 1.

Illustrative example at a 6% nominal rate on $10,000:

Going from yearly to monthly adds about 0.17 of a point a year. Going from monthly to daily adds about 0.015 of a point. Now compare that with the rate itself: the same $10,000 at 5% for thirty years reaches about $43,219, more than $14,000 less than at 6%. The rate and the time dominate; frequency is a refinement on top of them.

So when an offer leads with daily compounding, ask for the effective annual rate and put it beside the effective annual rate of the alternative. That single figure settles the frequency question. On a loan, the same arithmetic runs the other way: more frequent compounding at the same nominal rate costs you more.

How does Canadian law handle compounding on loans and mortgages?

The federal Interest Act sets two disclosure rules worth knowing. We read both on Justice Laws Canada on 29 September 2026.

Section 4 covers written contracts other than mortgages on real property or hypothecs on immovables. When a contract states interest at a rate per day, week, month or any period shorter than a year, it must also state the equivalent yearly rate. If it does not, no interest above 5% a year can be charged, paid or recovered on the principal.

Section 6 covers mortgages and hypothecs repaid with blended payments of principal and interest. The mortgage must state the principal and the rate of interest calculated yearly or half-yearly, not in advance. If it does not, no interest at all can be charged on the principal advanced.

That is why you will see Canadian mortgage rates described as compounded semi-annually, not in advance. Our reading of section 6 is that it requires the statement; it does not force every lender to compound half-yearly. Your own mortgage contract says which convention applies. Illustrative example: 5% compounded half-yearly works out to about 5.0625% a year, or about 0.4124% a month. The same 5% compounded monthly would be about 5.116% a year.

One more Canadian feature changes the arithmetic of a mortgage. A Canadian mortgage is repaid over a long amortization but renewed at the end of each term, so the rate can change at every renewal. A thirty-year calculation at one fixed rate describes a mortgage that does not exist here. Run it again at a higher rate for the years after your current term.

How accurate is the rule of 72?

Divide 72 by the yearly rate and you get a quick estimate of how many years a steady balance takes to double. It is a mental shortcut, not a calculation, and it is close enough across the rates you will meet in daily life.

It runs backwards too. If someone says an amount will double in twelve years, 72 divided by 12 tells you the rate they assumed: about 6% a year. That lets you test a claim in your head while it is still being made.

And it runs against you. An unpaid balance compounding at an effective 18% a year doubles in a little over four years. Inflation at 3% halves what a dollar buys in about 24 years. The shortcut is the same; only the direction changes.

How do regular contributions compound?

Each deposit starts its own compounding from the day it arrives. Money put in during year one has thirty years to grow; money put in during year thirty has almost none. The lump-sum formula cannot show that, so there is a second formula for equal deposits made at the end of each year:

• FV = PMT x ((1 + r)^t minus 1) divided by r

PMT is the amount deposited each year, r is the yearly rate as a decimal, and t is the number of years. For monthly deposits, use a monthly rate and the number of months instead.

Illustrative example: $2,000 deposited at the end of each year for 20 years, growing at 5% a year with no tax or fees. You put in $40,000. The formula gives about $66,132, so about $26,132 is growth. Carry the same deposits on for 30 years and you put in $60,000 against a result of about $132,878.

Steady deposits are the part of the result you control. A deposit made on schedule is your decision; the timing of markets is not. The amount you can keep up for decades matters more than the amount a projection suggests you could manage in a good year.

Which matters more: rate, time or contributions?

All three matter, and the honest answer depends on the numbers. The slogan that time always beats rate is not true, and the table shows why.

Illustrative example: $10,000 left alone, with no tax or fees.

In this example one percentage point of rate is worth about five years of time. Neither wins by default.

The same is true of the famous early-starter comparison. Illustrative example: one saver deposits $1,000 at the end of each year for years 1 to 10, then stops and leaves the money alone. A second saver deposits nothing for ten years, then $1,000 a year for years 11 to 30. Both are measured at the end of year 30.

At 6% the early saver ends ahead with half the deposits. At 5% they are nearly even. At 4% the later saver wins. So starting early helps a great deal, and it does not beat everything else automatically. Starting earlier and earning a higher rate both matter. Time is the one you control.

There is an uncomfortable part too. The years that count most for compounding can be the years when income is lowest and demands are highest: student debt, a first home, young children. Treating an early start as a question of discipline ignores that. Start with what you can keep up, and raise it when you can. A modest deposit kept up for decades does more than a larger one abandoned in year four.

How does tax change compounding in Canada?

Tax does not change the arithmetic. It changes how much of each year's growth stays in the base to keep compounding. Where the money sits decides the tax, and each place has its own rule. We describe them; we do not rank them.

The first row surprises people. Under the Canada Revenue Agency's line 12100 guidance, a five-year compound GIC held in a regular account produces taxable interest every year, even though you cannot touch the money until it matures. You pay tax on growth you have not received. Quebec residents report the same interest on their Revenu Québec return as well.

Illustrative example of the drag this creates. Assume interest at 5% a year on $10,000 for thirty years. Left untaxed while it grows, it reaches about $43,219. Now assume the interest is taxed every year at a combined rate of 40%, a figure chosen for illustration and not any province's actual rate, with the tax paid out of the growth. The after-tax growth is 3% a year, and the result is about $24,273. Same money, same rate, same years. What differs is where the tax is paid and when.

The registered plans do different jobs, with different contribution rules, withdrawal rules and eligibility. The practice behind this site is not registered to rank them against each other or against anything else. Questions about which fits you belong with a professional licensed to advise on registered plans, and questions about tax belong with an accountant.

What happens when you take money out?

A withdrawal lowers the balance that earns future growth. The balance left in place keeps compounding. Nothing restarts.

Illustrative example: $10,000 at 6% a year for thirty years reaches about $57,435 if left alone. Suppose instead you take $3,000 out at the end of year eight, when the balance is about $15,938. The remaining $12,938 keeps compounding and reaches about $46,624 at year thirty. The gap of about $10,811 is not a penalty for restarting. It is exactly the $3,000 plus the 22 years of growth that $3,000 would have earned.

That is the true cost of using savings to pay for something: the purchase price plus the growth the money would have produced, which is the idea behind opportunity cost. It is a real cost. It is not always the larger one. Borrowing instead leaves the savings in place but adds interest, fees and repayment risk, and you have to compare the two honestly, with both costs counted.

Missed deposits work the same way. Illustrative example: $2,000 a year for thirty years at 5% reaches about $132,878. Skip the deposits in years 11, 12 and 13, which is an ordinary life with a job change or a new child in it, and the result is about $118,427. The $6,000 not deposited costs about $14,451 by the end, because each missing deposit also misses its growth. Ask any projection what happens to its figure with three years missed.

When does compounding work against you on debt?

Debt compounds when its terms add unpaid interest to a balance that itself carries interest. Whether and how fast that happens depends on the agreement and on what you pay, so read your own contract rather than assuming.

Credit cards are one place people meet it. The Financial Consumer Agency of Canada explains the main rules:

• You pay interest if you do not pay your balance in full by the due date.
• Federally regulated financial institutions must give a grace period of at least 21 days on new purchases.
• Cash advances have no interest-free grace period; interest runs from the day you take the advance until you repay it.
• Your statement must show how long it would take to pay off the balance paying only the minimum, for federally regulated institutions.

The FCAC gives its own example: a $2,000 balance at 18%, paying only a $60 minimum, takes 3 years and 11 months to clear and costs $793 in interest. Paying $160 a month clears it in 1 year and 2 months for $231 in interest. The difference comes from how long the balance stays outstanding, and a balance that stays outstanding is a balance that keeps charging interest.

Set that beside savings. Growth at a modest rate does not keep up with a balance charging a high one. Where both exist, the rates you actually pay and earn decide which to deal with first, and the gap between them can be wide. Interest paid to a lender leaves your household for good, which links this idea to capital recovery: money spent on interest is capital that does not come back to you.

What are the three ways a projection overstates compounding?

Nothing is wrong with the formula. Projections go wrong in what they feed it, and three habits account for the gap between the chart and the life.

The first is showing nominal dollars. A figure thirty years out, before inflation, describes a number, not what it buys. At an assumed 3% inflation, $57,435 in thirty years buys about what $23,662 buys today. Ask whether a projection is in today's dollars or future dollars, and compare real with real.

The second is leaving out tax and fees. Growth quoted before tax, fees and trading costs is growth nobody received. Both compound against you. Illustrative example: $10,000 growing at 6% a year reaches about $57,435 in thirty years. If fees and costs take one percentage point off the yearly growth, it reaches about $43,219. The difference, about $14,215, is nearly five times the $3,000 that one percent of the starting $10,000 comes to over thirty years. A fee is not wrong in itself; it belongs inside the projection, not in a footnote. How advice fees are charged is explained under what a wealth manager charges.

The third is drawing a smooth, uninterrupted path. A projection at one constant rate hides the fact that real returns vary, and that the order of good and bad years matters once you start withdrawing: two paths with the same average can end very differently if the bad years come early in the withdrawal phase, because each withdrawal during a decline sells at a low point. The smooth path also assumes you never miss a deposit and never take money out, as the section above showed.

None of this makes compounding untrue. It makes every presentation of it worth reading slowly, and it makes the part a contract guarantees more interesting than the part it projects.

Where does compounding happen, and what protects it?

Compounding happens wherever earnings are added to a base and left there. That includes deposits that earn interest and GICs that reinvest it. It includes registered plans whose growth stays in, and funds whose distributions are reinvested. It also includes the cash value inside a permanent life insurance contract, while that contract stays exempt under the Canadian rules. The label on the product matters less than one question: does the growth stay in, and earn in turn?

The practice behind this site cannot tell you which of these to choose, and the reason is a licence, not a preference. It is not registered with the Canadian Investment Regulatory Organization and does not give securities advice. Which option fits you depends on your horizon, your circumstances and your tax position, and a person licensed for that question who knows those facts should answer it.

What can be said is what stands behind each promise, because a guaranteed figure is only as good as the institution that owes it.

• Deposits at an institution that belongs to the Canada Deposit Insurance Corporation: eligible deposits are insured up to $100,000 per insured category. The limit includes principal and interest. GICs and other term deposits can be eligible. The categories include deposits in one name, joint deposits, and deposits in a TFSA, RRSP, RRIF, RESP, RDSP or FHSA. Each category is insured separately. Mutual funds, stocks, bonds, ETFs and cryptocurrencies are not covered. Ask the institution whether it is a CDIC member.
• Life insurance from an insurer authorized in Canada: every such insurer must belong to Assuris. For a whole life policy, Assuris protects up to $1,000,000 or 90% of the promised death benefit, whichever is higher. It also protects up to $100,000 or 90% of the promised cash value, whichever is higher. Both are calculated on the values net of any policy loans.

Solvency supervision follows the insurer's charter: the Office of the Superintendent of Financial Institutions for a federally incorporated insurer, and the home province for a provincially incorporated one, which is the Autorité des marchés financiers in Quebec. A guarantee in a contract is a promise by one company, and these are the protections behind that promise.

Does value inside a specially designed, high-cash-value, participating whole life insurance policy compound?

Yes, in the ordinary sense, and three figures inside it need to be kept apart.

The guaranteed cash surrender value follows a schedule written into the contract. It grows on a base that includes earlier growth, and under the Income Tax Act that growth is not taxed each year while the contract stays exempt. The basic death benefit is also set by the contract. The Autorité des marchés financiers describes participating premiums as fixed for the period the contract requires them, with the basic insurance amount generally guaranteed.

Dividends are the second figure. The AMF is plain about them: dividends under a participating policy are not guaranteed, the insurer may reduce them, and in some years there may be none. Depending on the option chosen, dividends can buy paid-up additions, which raise later cash values and coverage, or be paid out another way. How they work is set out under dividend-paying life insurance.

The illustration is the third figure. It shows the guaranteed values plus dividends projected on assumptions, and the AMF notes that you will usually receive a realistic scenario and an adverse one. A dividend scale interest rate published by an insurer is an input to the dividend formula. It is not your rate of return.

Two plain facts sit beside the compounding. The early years are slow, because the insurer's acquisition and insurance costs are charged first, so the cash value sits below the premiums paid for a period; the contract's guaranteed column tells you how long. And the contract is life insurance first. It is not an investment, a deposit or a savings account, and it is worth buying only if you need the coverage and can carry the premiums for the long term. The AMF itself suggests asking whether you would be better served by less expensive insurance and saving the difference in a TFSA, RRSP, RESP or pension plan. That is a fair question to put to any proposal, including one from us.

What changes when you borrow against a policy instead of withdrawing?

Borrowing does not avoid interest. It changes who is paid, and it leaves the policy's values in place under the contract instead of reducing them.

Whether the part of the value that secures a loan earns the same dividends as the rest depends on the contract, so ask the insurer for that provision in writing. How a loan works day to day is on policy loans, and the tax detail is on when a policy loan becomes taxable.

With that on the table, here is how the idea connects to compounding. When you pay for a car or a renovation out of savings, the base shrinks and its future growth goes with it. When you borrow from an outside lender, the interest goes to that lender. The approach behind Infinite Financial Sovereignty®, a registered trademark of Jose Salloum, is aimed at that choice for a person who also needs permanent life insurance: the insurer advances money against the policy, the policy's values keep following the contract, and repayments to the insurer reduce the loan, so more of the value is available again within the contract's limits.

It is not a higher rate, and any description that implies one has misdescribed it. It costs more than leaving capital alone would, the interest goes to the insurer, and the policy needs years of premiums before it holds much value to borrow against. Reading about it is free; the firm behind this site is paid by insurer commission if a policy is bought. The case against it, including the parts critics get right, is in objections and risks.

What should you ask of any compounding projection?

Five questions work on any projection, from anyone, including one from us.

1. Is it nominal or real? A thirty-year figure that ignores inflation overstates what the money will buy. Unless the projection says it is in today's dollars, assume it is not.
2. Is it gross or net? Before or after tax, fees and costs. Those compound too, and a gross figure set beside a net one compares two different things.
3. What does it assume about deposits, withdrawals and a steady rate? Check whether it includes later deposits, withdrawals, changing rates, fees, tax and inflation, and ask for a second scenario with a plausible interruption, such as three missed years.
4. What is guaranteed and what is assumed? Where a contract has a guaranteed floor, that floor does not depend on anyone's rate assumption, though it does depend on the company that owes it and on the protections described above. Any figure above the floor rests on assumptions, and the two should never be shown as one number.
5. What happens if the assumed rate is one point lower? Over thirty years, one point changed the example above from about $57,435 to about $43,219. A presenter who cannot show you the lower figure has shown you one scenario and called it a plan.

A projection that answers all five is worth reading closely. One that answers none is a sales document with a chart in it.

What habits follow from the arithmetic?

These are principles, not a recommendation, because a recommendation needs to know you.

Start with what you can keep up. The years spent waiting for the perfect choice are years the arithmetic cannot give back, and a smaller amount kept up can do more than a larger one that stops.

Know which of your debts compound, and at what effective rate. A balance charging a high rate works against growth earning a lower one, and paying it down is a use of money with a known result.

Leave growth in place where you can, and when you need money, compare both costs: the growth a withdrawal gives up, and the interest, fees and risk a loan adds.

Know how tax treats each place your money compounds, and let a professional licensed for registered plans and an accountant for tax help you decide where it belongs.

Read every projection for its assumptions before its final number, and give guaranteed figures more weight than projected ones.

Compounding is a property of numbers. Whether a particular arrangement delivers it, at what cost, and whether it suits you are separate questions, and they need your facts. The other ideas under money decisions, explained the same way, are in money principles. This is general information, not investment, tax or legal advice, and all amounts are in Canadian dollars.