APR vs Effective Annual Rate

Two numbers describing the same money

Every rate quote has two layers. The APR, also called the nominal or stated annual rate, is the advertised number: 6%, 19.99%, whatever appears in the ad. The effective annual rate is what actually happens to a dollar over a full year once interest is added to the balance at some frequency and starts earning or charging interest on itself, which is ordinary compound interest at work.

If interest compounds exactly once a year, the two numbers are equal. The moment compounding happens more often, the effective rate climbs above the stated one, and the gap widens as the frequency increases. One caution on vocabulary: in Canadian cost-of-borrowing disclosure, "APR" can also fold certain mandatory fees into the rate. In this article, APR means the stated annual interest rate.

The formula, with a worked example

The conversion is one line: EAR = (1 + r/n)^n - 1, where r is the stated annual rate and n is the number of compounding periods per year.

Take 6% compounded monthly. Each month applies 6% / 12 = 0.5%. Twelve months compound to (1.005)^12 = 1.0617, so the effective annual rate is about 6.17%. The same 6% compounded semi-annually gives 6.09%, and daily gives about 6.18%. Notice the pattern: the first jump in frequency matters most, and the difference between monthly and daily is nearly invisible.

The Canadian mortgage quirk: semi-annual by law

Here is where Canada breaks from what most online calculators assume. Under the federal Interest Act, Canadian fixed mortgage rates must be expressed as interest compounded semi-annually, not monthly. A posted 5% Canadian fixed mortgage therefore works out to about 5.06% effective annually, while a US-style 5% mortgage compounded monthly works out to about 5.12%.

Same sticker, lower true cost on the Canadian side: the semi-annual convention produces a slightly lower monthly factor, and a slightly lower payment, than the American math at an identical quoted rate. The mechanics, the monthly factor, and the payment comparison are covered in detail under semi-annual compounding. The practical takeaway is simple: never run a Canadian fixed mortgage through an American calculator and trust the answer.

Credit cards: daily compounding, quietly

Credit cards sit at the other end of the frequency scale. A typical posted rate of 19.99% compounds daily on most Canadian cards, and (1 + 0.1999/365)^365 - 1 works out to about 22.1% effective annually. The card never advertises that number, but it is the one your balance obeys. This is one reason card debt grows faster than the posted rate suggests, and why paying the statement balance in full is worth so much.

Savings: the same math works for you

On the earning side, frequency is your friend. A high-interest savings account typically calculates interest daily and pays it monthly, so a stated 3% delivers about 3.05% effective annually. The boost is small, but the principle matters when comparing products: a GIC compounding annually and a savings account calculating daily are not paying the same thing at the same stated rate.

The comparison rule, and one common mix-up

When shopping, compare effective annual rates, or at minimum make sure both quotes use the same compounding basis. Two loans at "6%" can cost different amounts; two savings rates at "3%" can pay different amounts. The EAR collapses every quote onto one honest scale.

Do not confuse compounding frequency with payment frequency. Compounding frequency is how often interest joins the balance, and it sets the effective rate. Payment frequency is how often you send money, and it changes how fast the principal falls, not the rate itself. Paying a mortgage weekly instead of monthly barely changes the interest math; what saves real money is paying more per year, which is the actual engine behind accelerated biweekly payments.