Money basics

APR vs APY: The Two Percentages That Decide Everything

The same 6 percent can pay six different amounts. How compounding frequency turns a rate into a yield, and why loans and savings accounts are quoted differently.

By the Euphoria team · 2026-07-25 · 8 min read

A rate is two facts, and the advertisement gives you one

Write down 6 percent. You have not yet described how much money changes hands, because a rate on its own is only half a specification. The other half is how often the interest gets applied, and until you know that, 6 percent can mean at least half a dozen different amounts.

That second half is the entire difference between the two acronyms you keep meeting. APR, the annual percentage rate, is a simple annualized rate: take the rate charged in each period and multiply up to a year. APY, the annual percentage yield, is the amount you would actually end up with after a year, including the interest that earned interest along the way.

Same underlying rate. Two conventions for reporting it. One of them is always the larger number, and the gap between them is not a trick or a fee. It is a calendar.

• 6.00% a 6 percent rate applied once a year
• 6.18% the same 6 percent applied daily
• 24.79% what a 22.15 percent card rate costs when it compounds daily

What each one is defined to include

APR is the disclosure convention for borrowing. Under the Truth in Lending Act, implemented as Regulation Z, a lender has to quote you the cost of credit as a yearly rate, and on many loans that figure is required to fold in certain charges beyond interest, such as points and some origination fees. The CFPB's definition is worth reading once, because the useful part is what APR leaves out: it does not account for interest compounding inside the year.

APY is the disclosure convention for deposits. Under the Truth in Savings Act, implemented as Regulation DD, a bank advertising a savings account has to state the annual percentage yield, which by definition does include compounding within the year, assuming the balance stays put.

So the periodic rate is the raw fact, APR is that fact annualized without compounding, and APY is that fact annualized with compounding. Everything else in this article follows from those three sentences.

The arithmetic of frequency, worked out

Take a nominal 6 percent and split it across n periods a year. Each period applies a rate of 0.06 divided by n, and the year-end multiplier is that plus one, raised to the power n. Subtract one and you have the APY.

• Once a year: 1.06 to the power 1, so 6.000 percent.
• Twice a year: 1.03 squared is 1.0609, so 6.090 percent.
• Four times: 1.015 to the fourth is 1.061364, so 6.136 percent.
• Twelve times: 1.005 to the twelfth is 1.061678, so 6.168 percent.
• Every day: one plus 0.06 over 365, to the power 365, so 6.183 percent.

Two things are worth noticing, and the second one is the useful one.

The first is that more frequent compounding always pays more. The second is that it stops mattering almost immediately. Going from annual to semiannual buys you 9 basis points. Going from monthly all the way to daily buys you 1.5. Push the frequency to infinity and the answer converges on 6.1837 percent, which is the continuous compounding limit, and daily has already reached 6.1831. The marketing distinction between monthly and daily compounding is worth about one and a half hundredths of a percentage point, and anyone making a fuss about it is selling you a rounding error.

Why the gap is trivial at 6 percent and serious at 22

The size of the compounding effect scales with roughly the square of the rate, which means it is almost invisible on a savings account and very much visible on a credit card.

A credit card does not charge you its annual rate once a year. It divides that rate by 365 to get a daily periodic rate, then applies it to your balance every single day of the billing cycle. The Federal Reserve's G.19 consumer credit release put the average rate on card accounts assessed interest at 22.15 percent in its most recent quarterly reading, alongside 20.94 percent averaged across all accounts.

Divide 22.15 by 365 and the daily periodic rate is 0.060685 percent. Apply that every day for a year and the compounded result is 24.79 percent. The quoted number understates the real annual cost of carrying a balance by more than two and a half percentage points, and the law requires the quote to be the understated one.

A lender must quote you the lower convention and a bank must quote you the higher one. Both rules push the same direction.

The asymmetry that actually costs people money

Put the two disclosure regimes side by side and something awkward appears.

On a loan you are shown an APR, which excludes intra-year compounding and is therefore the smaller of the two possible numbers. On a deposit you are shown an APY, which includes compounding and is therefore the larger. Neither figure is dishonest and both are legally required. But if you compare a loan quoted at 7 percent against a savings account quoted at 4 percent and conclude the spread is 3 points, you have compared a number built to look small against a number built to look large.

To compare them properly you have to put both on the same footing. A 7 percent loan compounding monthly costs about 7.23 percent a year in APY terms. A savings account advertising 4 percent APY is already stated that way. The real spread is closer to 3.2 points than 3. On a mortgage-sized balance over decades, a rounding habit like that is not small.

How carrying a card balance compounds daily

The mechanics matter because one habit switches the whole machine on or off.

Most issuers compute finance charges using an average daily balance method: add up what you owed at the end of each day in the cycle, divide by the number of days, then multiply by the daily periodic rate and by the days in the cycle. The CFPB walks through this calculation with a worked example.

Carry $1,000 for a 30-day cycle at that 0.060685 percent daily rate and you are charged $18.37. Simple monthly interest on the same rate would have been $18.21. The 16 cents is the compounding, and on one month it is nothing. The reason it becomes real is the grace period.

If you pay your statement balance in full every cycle, most cards charge no interest on new purchases at all, so the entire daily compounding machine sits idle. The moment you carry a balance, you typically lose that grace period, and new purchases start accruing from the day they post rather than from the due date. That is the switch. It is not the rate that changes, it is the number of days the rate is applied to.

Thirty years of the same rate, two ways

To see the compounding effect at the scale where it stops being a rounding error, hold the rate constant and let the years run. Here is $1,000 at 6 percent, compounded once a year against compounded daily.

After one year the difference is $1.83. After ten years it is $31. After thirty years the annual version reaches $5,743.49 and the daily version reaches $6,048.75, a difference of $305.26. Nothing changed except when the interest got credited.

That is the honest scale of it. Frequency is a real effect that grows with time and with the rate, and it is also much smaller than the effect of the rate itself, or of how long you leave the balance alone. If you are choosing between accounts, the headline rate and the fees deserve most of your attention, and the compounding schedule deserves a glance.

Reading the next percentage you meet

Three questions will settle almost any rate you are shown.

First, which convention is this? If it is a loan or a card, it is almost certainly an APR and the true annual cost is higher. If it is a deposit, it is an APY and already includes compounding.

Second, how often is it applied? Divide by that number to recover the periodic rate, which is the only figure that describes what happens to your balance on an actual day.

Third, is the comparison I am about to make apples to apples? Two rates in different conventions cannot be subtracted, and the difference is always in the direction that makes borrowing look cheaper relative to saving than it is.

Euphoria's lessons let you turn the frequency dial yourself: set a rate, choose how often it compounds, and watch the same nominal percentage produce different balances, which is a faster way to internalize this than any formula.