Compound interest explained: how it grows savings, time and debt

According to the FCAC, with compound interest your initial deposit earns interest; that interest is added to your savings; you then earn interest on the total. In short: interest on interest. The more often interest is compounded, the faster the balance can grow, all else equal. Formula for a single deposit (periodic compounding): A = P × (1 + r/n)^(n×t) where A is the final amount, P the starting principal, r the annual rate as a decimal, n the number of compounding periods per year, and t the number of years. Simple vs compound (illustration). For $5,000 at 3% for 20 years (hypothetical rate): • simple interest: $5,000 × (1 + 0.03 × 20) = $8,000; • compounded once a year: $9,030.56; • difference: $1,030.56 from interest earned on interest alone. These figures do not predict any market return.

The FCAC illustrates a savings account as follows: you deposit $100 each month, annual rate 2%, compounded monthly (about 0.167% per month, or 2% ÷ 12). • After month 1: about $0.17 interest on $100. • After month 2: interest on $200 plus the $0.17 already earned → about $0.33. • By the end of year 1: $13.08 total interest on $1,200 deposited. Our script also matches the FCAC’s approximate cumulative-interest table: • year 1: $1,200 deposited, $13.08 interest; • year 2: $2,400, $50.64; • year 3: $3,600, $113.19; • year 4: $4,800, $201.22; • year 5: $6,000, $315.24. The FCAC notes that actual results depend on how the institution calculates interest (for example, days in the month). Ask how often interest is compounded, and read the account agreement: the rate may vary by balance, and an introductory rate may fall later.

The advertised rate is usually annual, but compounding may be monthly or daily. Per the FCAC, daily compounding grows a balance faster than monthly compounding at the same advertised annual rate. Illustration ($5,000, 5%, 10 years, hypothetical rate): • annual compounding: $8,144.47; • monthly: $8,235.05; • daily: $8,243.32. The gap is modest over 10 years at 5%; it grows with time, rate and principal. Compare frequency, not only the advertised rate.

With the same $5,000 at 3% compounded annually (hypothetical rate): • 10 years → $6,719.58 ($1,719.58 interest); • 20 years → $9,030.56 ($4,030.56 interest); • 30 years → $12,136.31 ($7,136.31 interest). Growth is not linear: later years add more interest because the balance is larger. Starting earlier allows more compounding periods; that is arithmetic about time, not investment advice.

GetSmarterAboutMoney.ca (Ontario Securities Commission) presents the Rule of 72 as a quick way to estimate how long it takes to double money: divide 72 by the annual rate in percent. Example: at 6%, 72 ÷ 6 = 12 years. It is not exact; at 3%, the rule gives 24 years while the exact calculation (ln 2 / ln 1.03) is about 23.45 years. Useful for a mental estimate, not for a contract.

According to the FCAC, you pay interest if you do not pay the balance in full by the due date, and you keep paying interest until the balance is paid off. Federally regulated institutions must provide an interest-free grace period of at least 21 days for purchases; that grace period does not apply to cash advances, cash-like transactions or balance transfers. The FCAC gives possible order-of-magnitude examples of 19% on purchases and 22% on cash advances (examples, not your rates). Educational illustration (hypothetical rate and payments; your issuer’s method may differ): $5,000 balance at 20% per year, interest calculated monthly on the balance, no new purchases: • $100 per month → about 9 years and 1 month, $5,840 interest (about $10,840 repaid in total); • $200 per month → about 2 years and 9 months, $1,522 interest; • difference: about $4,318 less interest and 76 months sooner. The FCAC advises paying the statement balance in full by the due date when you can; otherwise, paying as much as possible as early as possible reduces interest. See also the FCAC Credit Card Payment Calculator.

According to the FCAC, interest in an ordinary savings account is usually taxable; the institution issues a T5 slip. For longer-term savings, the FCAC says to consider a Tax-Free Savings Account (TFSA): you do not pay tax on the interest you earn or, generally, on withdrawals. GetSmarterAboutMoney.ca also notes that in an RRSP or TFSA, earnings can grow tax-free while the money stays in the account. These are general tax facts, not a recommendation to open an account or buy a specific product. To compare RRSP and TFSA, see RRSP or TFSA in 2026. The Bank of Canada offers an investment calculator that uses annual compounding and a default inflation rate of 2% (the mid-point of its inflation-control target). Illustration: $5,000 at 3% for 20 years is about $9,030.56 in nominal dollars; in purchasing-power terms (2% inflation), the real value is about $6,077. A positive nominal rate does not guarantee a gain in purchasing power. To try other scenarios, use our compound interest calculator. For the interest/principal split on an amortized loan, see Mortgage amortization explained.