APR vs. APY: Why the Same Rate Shows Two Different Numbers

You look at a savings account advertising 4.00% APY and a credit card charging 22.9% APR, and reasonably assume both numbers mean the same kind of thing.

They do not. APR vs. APY is a genuine difference with real money attached, and — not coincidentally — institutions tend to quote whichever one makes their product look better.

APR vs. APY in one sentence each

APR (Annual Percentage Rate) is the simple annual rate, ignoring the effect of compounding within the year. On loans it also includes certain mandatory fees.

APY (Annual Percentage Yield) is the effective annual rate, including the effect of compounding within the year.

APY is always equal to or higher than the equivalent APR. They are only identical when interest compounds exactly once a year.

The arithmetic

The conversion is:

APY = (1 + APR/n)^n − 1

  n = number of compounding periods per year

Take a 12% APR at different compounding frequencies:

Same headline 12%. The actual cost or return ranges from 12.00% to 12.75% depending purely on how often interest is calculated.

The gap widens as rates rise. At 22.9% APR compounded daily — standard for credit cards — the APY is roughly 25.7%. That is nearly three percentage points of real cost that the advertised number does not show.

Which one gets quoted, and why

Here is the pattern, and once you see it you cannot unsee it.

Savings accounts advertise APY. Higher number, and it flatters the product. This is also the number regulators generally require for deposits, precisely so consumers can compare like with like.

Credit cards advertise APR. Lower number. Your statement will say 22.9% APR; the effective annual cost of carrying a balance is closer to 25.7%. Nothing dishonest is happening — the daily periodic rate is disclosed — but the headline understates the reality.

Loans advertise APR, and here it is genuinely useful. For mortgages and personal loans, APR is required to bundle in origination fees and certain costs, which makes it a better comparison tool than the raw interest rate. A 6.0% mortgage with $4,000 of fees might carry a 6.3% APR; a 6.2% mortgage with no fees might be 6.2% APR and actually cheaper.

So the rule is not "APY good, APR bad." It is: know which one you are looking at, and never compare an APR to an APY directly.

Where this actually costs you money

Comparing a savings account to a loan. A 4.00% APY savings account and a 4.00% APR loan are not the same rate. The loan, if it compounds monthly, effectively costs about 4.07%.

Comparing two savings accounts quoted differently. Some institutions still quote "interest rate" (an APR-like figure) alongside APY. A 4.9% "rate" compounded monthly is a 5.01% APY. A competitor's flat 4.95% APY is worse than it looks next to that.

Underestimating card debt. People budgeting a payoff at "23%" are working with a number about 11% too low in relative terms. Over a multi-year payoff on a large balance, the difference is real. How credit card interest actually works walks through the daily calculation.

Overestimating investment returns. Some platforms advertise annualised returns using different conventions. Check whether a quoted figure is nominal or effective before comparing.

A quick way to convert in your head

You do not need the formula for most situations. For monthly compounding, a decent approximation is:

APY ≈ APR + (APR² ÷ 2)     [rates as decimals]

  5% APR  ->  0.05 + 0.00125  =  5.13%   (actual: 5.12%)
  23% APR ->  0.23 + 0.0265   =  25.65%  (actual: 25.59%)

Close enough to make a decision with. The practical takeaway is that the gap is trivial at low rates and significant at high rates — which is exactly why it matters most on credit card debt and least on a savings account.

The related terms you will meet

Nominal rate — the stated rate before compounding. Effectively the same idea as APR in most contexts.

Effective annual rate (EAR) — the same idea as APY, used more often in a lending context. If you see EAR, treat it as APY.

Daily periodic rate — APR ÷ 365. This is the number credit cards actually apply each day, and it is usually printed in small type on your statement.

Real rate — the return after inflation. A 4% APY during 3% inflation is roughly 1% real. This is a different adjustment entirely and it stacks on top: you can have a high APY and still lose purchasing power, which is the core argument in saving vs. investing.

What to do with this

Three habits cover almost every case:

1. When comparing savings accounts, insist on APY for both. If one is quoted as a plain interest rate, convert before comparing.
2. When comparing loans, use APR — it includes fees, which the raw rate does not.
3. When estimating what card debt actually costs you, add roughly 10% to the APR as a mental adjustment for daily compounding.

None of this changes what you should do about high-interest debt — the answer is still to clear it first. It just means the guaranteed return from doing so is even better than the sticker rate suggests.