APR vs APY: what each rate actually counts

Q: How do I convert APR to APY?

Divide the APR by the periods in a year, add one, raise to that number of periods, subtract one. For 24% charged monthly: 1.02^12 - 1 = 26.82%. This ignores any fees included in a loan APR.

One is a yearly rate before compounding, the other after it. Which one you are shown depends on whether you are borrowing or saving.

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APR vs APY comes down to one word: compounding. An APR is a yearly rate before interest is charged on interest; an APY is the yearly rate after it. That is why the same monthly charge produces a smaller APR than APY, and why loans are quoted in one and savings in the other. If you have an APY, it goes straight into the compound growth calculator, which takes exactly that kind of rate.

What APY means

In the US, the annual percentage yield on a deposit account is defined by the Truth in Savings rules (Regulation DD). Its formula, in Appendix A, is the interest a deposit earns over its term, turned into a yearly rate with compounding counted. For an ordinary savings account the term is taken as 365 days, and the rule tells the bank to assume that all the principal and interest stay in the account and that nothing is added or taken out.

So an APY is a promise about one clean year: put $10,000 in at 4.5% APY, leave it alone, and after twelve months there is $10,450. How often the bank credits interest — daily, monthly — is already inside that number. That is the point of it: two accounts that compound differently can be compared directly by their APY.

It is still a snapshot. Most savings rates are variable, so the APY describes the rate as it stands, not what the account will earn over a year in which the rate changes.

What APR means

An annual percentage rate is a borrowing figure, set by the Truth in Lending rules (Regulation Z), and it means slightly different things for different kinds of credit.

On a credit card, the APR is the card's periodic rate multiplied by the number of periods in a year. Section 1026.14(b) says so directly. A card charging 2% a month has a 24% APR. Nothing is compounded in getting there.
On a mortgage or other loan, the APR also folds in some of the cost of getting the loan. The CFPB's explanation is that it reflects the interest rate plus points, broker fees and other charges, which is why it is usually higher than the loan's interest rate.

In both cases the APR is a simple yearly figure. It is useful for comparing one loan with another, but it is not the rate your balance grows at if interest is charged on interest.

APR vs APY: the same rate, two numbers

Take a card with a 24% APR, charged monthly at 2%. If a $5,000 balance sat for a year with the interest added to it each month, it would owe $6,341 at the end, not $6,200. The 2% in month twelve is charged on eleven months of earlier interest as well as the $5,000. Expressed as a yearly rate, that is 26.82%: the APY-style number behind the 24% APR.

The same conversion on a few quoted rates, each charged monthly at the APR divided by twelve:

6% APR → 6.17% a year compounded
22% APR → 24.36%
24% APR → 26.82%
29% APR → 33.18%

The gap grows with the rate. At mortgage-level rates it is a fraction of a point; at credit-card rates it is several points. The loan repayment calculator shows this figure for whatever rate you enter, under the heading “one thing about the rate”.

How compounding frequency changes the APY

Start from a 5% yearly rate before compounding and credit it at different frequencies:

Once a year: 5.00% APY
Quarterly: 5.09%
Monthly: 5.12%
Daily (365 times): 5.13%

Going from yearly to monthly adds just over a tenth of a point. Going from monthly to daily adds about a hundredth. Once interest is credited monthly, how much more often it compounds barely matters — which is why an APY, which already includes it, is the fair number to compare.

Which rate to put into a calculator

This is where the difference stops being academic, because calculators disagree about what their rate box means.

The growth tools on this site treat a rate as effective: 7% a year means the money is 7% bigger after twelve months. That is an APY in all but name, so an APY goes in unchanged. How the maths works explains why they use the exact monthly conversion rather than dividing by twelve. The loan and debt tools do the opposite: they take the rate a lender quotes and divide it by twelve, because that is how lenders charge it.

Mixing them up has a small but real cost. Suppose a savings account quotes 4.5% compounded monthly, which is a 4.59% APY. Type 4.5% into a growth calculator that expects an APY and $10,000 over twenty years comes out at $24,117. Type the true APY and it is $24,555. The difference, $438, is the compounding the first figure left out.

Common questions

Is APR or APY higher?

For the same underlying rate, the APY is higher whenever interest compounds more than once a year, because it counts interest on interest and the APR does not. On a loan, though, the APR can also include fees, so a loan's APR may sit above its own interest rate for a different reason.

Why do banks show APY on savings and APR on loans?

Because US rules ask for different figures. Regulation DD sets how the APY on deposit accounts is calculated; Regulation Z sets how the APR on credit is calculated. Each is a standard number so that like can be compared with like.

How do I convert APR to APY?

Divide the APR by the number of periods in a year, add one, raise it to that number of periods, and subtract one. For 24% charged monthly: 1.02 to the power of 12, minus 1, is 26.82%. This ignores any fees included in a loan's APR.

Does 4.5% APY mean I earn exactly 4.5% this year?

Only if the rate stays the same all year and nothing is added or withdrawn — the assumptions the APY formula is built on. Most savings rates are variable, so the year's actual interest can differ.

Does paying a card in full each month change this?

Yes. The gap between 24% and 26.82% only appears when interest is left on the balance and charged interest in turn. A balance cleared each month is not accumulating interest to compound.

Not financial advice. Worked examples assume a fixed rate, interest charged or credited monthly unless stated, and no fees. The US definitions are summarised from the regulations linked above; individual card and loan terms vary.