Understanding APR vs APY (with worked examples)

The one-sentence definitions

APR (Annual Percentage Rate) is the simple annual interest rate, without compounding. APY (Annual Percentage Yield) is the effective annual interest rate WITH compounding included. The difference between them is the magnitude of intra-year compounding — more frequent compounding produces a larger APY for the same APR.

APY is always greater than or equal to APR for the same nominal rate. The two are equal only when compounding happens just once a year. Daily compounding (typical for savings and credit cards) opens the biggest spread; monthly compounding (typical for mortgages and most loans) opens a smaller one.

The conversion math

APY = (1 + APR / n)^n − 1, where n is the number of compounding periods per year. For daily compounding, n = 365. For monthly, n = 12. For quarterly, n = 4.

Worked example: a savings account quotes a 5.00% APY. What's the underlying APR? Solve for APR: APR = n × ((1 + APY)^(1/n) − 1). With daily compounding (n=365), APR = 365 × ((1.05)^(1/365) − 1) ≈ 4.879%. The bank chose to advertise the APY because 5.00 looks better than 4.88 in a headline.

Reverse example: a credit card discloses a 22.99% APR with daily compounding. What's the effective APY you actually pay? APY = (1 + 0.2299/365)^365 − 1 ≈ 25.83%. That's nearly three percentage points the disclosure doesn't surface. Carry a $5,000 balance for a year and you pay $1,291 in interest, not the $1,150 the APR would suggest.

Why mortgages use APR and savings accounts use APY

APR on a mortgage is regulated under TILA (Truth in Lending Act) and is required to include certain financing costs — origination, discount points, mortgage insurance, prepaid interest — in addition to the note rate. That's why APR is always higher than the quoted note rate. The intent is to make APR a directly comparable number across lenders even when their fee structures differ.

APY on a deposit account is regulated under TISA (Truth in Savings Act) and requires the bank to disclose the effective annual yield assuming the rate stays constant for a year. This is the consumer-friendly direction: deposits compound in the saver's favor, so disclosing APY tells you what you actually earn.

Lenders pick the direction that flatters their product. A high APR with low APY looks worse than a comparable product whose APY is disclosed. A low APR-disclosed mortgage with high closing costs has a higher 'true' APR than the headline. Always ask for the disclosure document and read both numbers if they exist.

When you actually need to convert

Comparing a credit card to a HELOC. Credit card APR with daily compounding produces a meaningfully higher APY than a HELOC at the same APR with monthly billing. To compare apples-to-apples, convert both to APY and compare those.

Choosing between savings vehicles. A money market fund at 4.75% APY and a high-yield savings account at 4.85% APY are directly comparable — the APY math has already been done for you. If one product quotes APR instead, convert it first.

Sizing extra mortgage payments. The interest you save by paying down a mortgage early is at the loan's note rate (the APR before fees). The interest you would have earned by investing the same money is at your portfolio's APY (after compounding). Use both numbers in the comparison or you'll systematically underestimate one side.

Our APR vs APY converter handles all four common compounding frequencies and lets you toggle direction in one click.