APR vs APY: what is the difference?

APR and APY defined

APR, annual percentage rate, is the interest rate for a year without counting compounding. If you deposit $1,000 at 10% APR and take the interest out each time it is paid, you collect $100 over the year.

APY, annual percentage yield, is what you actually end up with after a year if the interest is left in and earns interest itself. It is sometimes called the effective annual rate. If that same 10% is paid monthly and reinvested, each month's interest is calculated on a slightly larger balance, and the year ends at about $1,104.71, a yield of 10.47%.

So the two numbers describe the same rate in different ways. APR tells you the headline rate; APY tells you the result after compounding.

The formula and a worked example

To turn an APR into an APY:

APY = (1 + r / n)ⁿ - 1

where r is the APR as a decimal (10% = 0.10) and n is how many times interest is paid and added to the balance each year. Going the other way, APR = n × ((1 + APY)^1/n - 1).

Here is the same 10% APR on a $1,000 deposit, compounded at different frequencies:

Two things stand out. Going from yearly to monthly makes most of the difference; going from weekly to daily adds very little. And at higher rates the gap widens: a 50% APR compounded daily is roughly 65% APY. To see compounding over several years, try the compounding calculator.

APR vs APY in crypto staking and lending

Crypto platforms quote both, and the choice is not always neutral. Staking, lending and liquidity pools often pay rewards daily or even every few minutes, so the APY can sit well above the APR, especially when rates are high. A product shown as "20% APY" and another shown as "18% APR" may be close to identical once you convert one into the other.

Some points worth checking before comparing yields:

• Does compounding happen by itself? APY assumes rewards are added back and keep earning. If you must claim and restake them by hand, and each claim costs a network fee, the real return can be closer to the APR, or below it.
• What currency are rewards paid in? A yield paid in a volatile token can be wiped out by a fall in that token's price. A high APY on a coin that halves in value is a loss in dollar terms.
• Is the rate fixed? Many crypto yields change daily. A quoted APY is often today's rate projected over a year, not a promise.
• Who holds the funds? Yield offered by a company that takes custody of your coins carries the risk of that company. See CeFi vs DeFi.

Which one should you look at?

Use the figure that matches what you will actually do:

• Earning interest and leaving it in: APY shows your real yearly return.
• Taking interest out as it is paid: APR is closer to what you will receive.
• Borrowing: loans are usually quoted in APR, which makes them look cheaper. The effective cost after compounding is the APY-style figure, and it is higher.

When two products quote different measures, convert one with the formula above before deciding. A headline rate on its own says nothing about risk, which is often the bigger difference between two yields.