How does compound interest work? A calculator and real examples
Compound interest is the most quoted idea in personal finance and one of the least shown. People hear "money makes money" without ever seeing the numbers line up. So here is the arithmetic, step by step, a calculator you can run with your own figures, and the part people skip: how compounding works on what you owe.
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Compound interest calculator
Run your own numbers
| Year | Put in so far | Balance | Interest so far |
|---|
Monthly deposits are added at the end of each month. The rate is held constant for illustration; real savings rates change, and investment returns are not guaranteed. The calculator ignores tax and fees, both of which reduce what compounds.
How compound interest works, step by step
Simple interest pays you only on the amount you started with. Put $1,000 in at 6% simple interest and you earn $60 every year, the same $60 forever. After 30 years: $1,000 + ($60 × 30) = $2,800.
Compound interest adds each year's interest to the balance, and the next year's interest is calculated on the new, bigger number:
| Year | Balance at start | Interest at 6% | Balance at end |
|---|---|---|---|
| 1 | $1,000.00 | $60.00 | $1,060.00 |
| 2 | $1,060.00 | $63.60 | $1,123.60 |
| 3 | $1,123.60 | $67.42 | $1,191.02 |
The extra is tiny at first: $3.60 in year two. But it never stops building. After 30 years of yearly compounding, the same $1,000 is about $5,743, more than double the simple interest result, without adding a single dollar.
The compound interest formula, in plain English
The standard formula is A = P × (1 + r/n)n×t, where:
- P is the starting amount (principal)
- r is the annual rate as a decimal (6% is 0.06)
- n is how many times a year interest is added (1 for yearly, 12 for monthly)
- t is the number of years
- A is what you end up with
Example: $1,000 at 6% compounded yearly for 3 years is 1,000 × 1.063 = 1,000 × 1.191016 = $1,191.02, matching the table above.
Monthly deposits: what $200 a month becomes
Most people do not drop in one lump sum; they add a bit every month. Here is $200 a month at a hypothetical 6% a year, compounded monthly, with each deposit made at the end of the month:
| Time | Total put in | Ending balance | Interest earned |
|---|---|---|---|
| 10 years | $24,000 | $32,776 | $8,776 |
| 20 years | $48,000 | $92,408 | $44,408 |
| 30 years | $72,000 | $200,903 | $128,903 |
Look at the last decade. Going from 20 to 30 years adds $24,000 of deposits but about $108,495 to the balance ($200,903 minus $92,408). By year 30, interest makes up roughly 64% of the total. (An earlier version of this page showed slightly higher figures that assumed deposits at the start of each month; these figures use end-of-month deposits.)
Why time does the heavy lifting
Compare two savers at the same hypothetical 6%:
- Early saver: $200 a month from age 25 to 35 (10 years, $24,000 put in), then nothing more, left to compound until 55. Balance at 55: about $108,495.
- Later saver: $200 a month from age 35 to 55 (20 years, $48,000 put in). Balance at 55: about $92,408.
The early saver put in half as much and ends up about $16,087 ahead, because their first deposits had 30 years to compound instead of 20. The lesson is not about any particular product. It is that each dollar's growth depends on how long it sits, and that fees or interest you pay along the way shrink the base that compounds.
Does compounding frequency matter?
A little. Here is $10,000 at 4% for 10 years, no deposits:
| Interest added | Balance after 10 years | Interest earned |
|---|---|---|
| Simple (no compounding) | $14,000.00 | $4,000.00 |
| Yearly | $14,802.44 | $4,802.44 |
| Monthly | $14,908.33 | $4,908.33 |
| Daily | $14,917.92 | $4,917.92 |
Going from simple to yearly compounding is worth $802. Going from monthly to daily adds less than $10. The rate and the number of years matter far more than the frequency. When you compare savings accounts, check how the rate is calculated and paid, and whether a higher rate is a promotional one that ends. Our guide to how a HISA works covers that.
The rule of 72
Divide 72 by the annual rate to estimate how many years it takes money to double. At 6%: 72 ÷ 6 = 12 years. The exact answer with yearly compounding is about 11.9 years, so the shortcut is close. It works in reverse too: at a 19% card rate, 72 ÷ 19 is about 3.8 years for an unpaid balance to double if interest keeps compounding and nothing is paid.
Compound interest on debt: the same math, pointed at you
When you carry a balance, unpaid interest is added to what you owe, and then that interest gets charged interest too. FCAC uses 19% as an example rate for credit card purchases and 22% for cash advances.
Take a $2,000 balance at 19%, with interest added monthly and nothing paid:
- Month 1 interest: $2,000 × 0.19 ÷ 12 = $31.67
- Month 2 interest: $2,031.67 × 0.19 ÷ 12 = $32.17
- After 12 months: about $2,414.90, so $414.90 of interest on $2,000
Your card agreement sets how interest is calculated and charged, so treat this as an illustration of the direction, not your exact bill. The protection is the grace period: FCAC says federally regulated issuers must give at least 21 days interest-free on new purchases when you pay the full balance by the due date. Cash advances get no grace period at all. Our guides to the credit card grace period and the minimum payment trap show the numbers on a real statement.
Where compounding happens in Canada
- Savings accounts and GICs. Interest is added on a schedule set by the institution. Interest earned outside a registered account is generally taxable; see is HISA interest taxable.
- TFSA. The CRA says contributions and any income earned in a TFSA through interest, dividends or capital gains are generally tax-free, even when you withdraw. That lets the full amount keep compounding. See your TFSA room by birth year.
- RRSP and FHSA. Growth is sheltered while it stays in the plan, with different rules on the way out; our RRSP vs TFSA and FHSA guides compare them.
- RESP. Government grants are added on top of contributions and grow inside the plan; see the RESP grant guide.
These are account types to understand, not recommendations; what you hold inside them is your own decision. More tools are on the tools page.
How to calculate compound interest
- Write down the starting amount, the annual interest rate as a decimal, and how often interest is added each year.
- Divide the annual rate by the number of times interest is added to get the rate per period.
- Add 1 to the rate per period and raise it to the power of the total number of periods.
- Multiply the starting amount by that number to get the ending balance.
- Subtract the starting amount to see how much interest was earned.
- For regular deposits, use the calculator above, which adds each monthly deposit and compounds it.
Questions people ask
How does compound interest work?
Interest is added to your balance, and the next round of interest is calculated on the bigger balance. At 6% a year, $1,000 earns $60 in year one, then $63.60 in year two because it is now earning on $1,060.
What is the difference between simple and compound interest?
Simple interest is paid only on your original amount. Compound interest is paid on the original amount plus the interest already added. $1,000 at 6% for 30 years grows to $2,800 with simple interest and about $5,743 with yearly compounding.
Does compounding frequency matter?
Yes, but less than the rate and the time. $10,000 at 4% for 10 years grows to $14,802.44 compounded yearly, $14,908.33 compounded monthly and $14,917.92 compounded daily.
What is the rule of 72?
A shortcut for how long money takes to double: divide 72 by the annual rate. At 6%, 72 divided by 6 is 12 years. The exact answer at 6% compounded yearly is about 11.9 years.
Why does starting earlier make such a difference?
Because each dollar has more years to compound. At a hypothetical 6%, $200 a month for 10 years and then left alone for 20 more grows to about $108,495, more than $200 a month for 20 years starting a decade later, about $92,408, despite half the deposits.
How does compound interest work on a credit card?
Unpaid interest is added to what you owe and then charged interest itself. FCAC uses 19% as an example purchase rate. On a $2,000 balance at 19%, if interest is added monthly and nothing is paid, the balance grows to about $2,414.90 in a year.
Is interest earned in a TFSA taxed?
The CRA says contributions and any income earned in a TFSA through interest, dividends or capital gains are generally tax-free, even when withdrawn. That lets the full amount keep compounding.
A monthly fee you never notice is money that never gets to compound. Looni scans your transactions for fees, interest charges and forgotten subscriptions, with proof for each one. Read-only, no advice.
Sources
Financial Consumer Agency of Canada, How credit cards work (example rates of 19% for purchases and 22% for cash advances, minimum 21-day interest-free grace period, no grace period on cash advances). Canada Revenue Agency, What is a TFSA (contributions and income earned are generally tax-free, even when withdrawn). All other figures are our arithmetic using the standard compound interest formula, checked in Python; the rates are hypothetical and for illustration only.