APR vs APY: The Difference, With the Math and Examples

A savings account and a credit card each quote a yearly rate, yet neither number tells you what a year of balance actually does. The gap between the quoted rate and the real one is compounding, and APR and APY sit on opposite sides of it. Below: what each term means in federal rule text, the APY formula with a worked case, a calculator, worked examples at two rates, how loan fees change APR, and what a “good” APY or APR can be compared with. The money section holds the formulas next to this one.

What APR and APY each measure

The annual percentage yield, or APY, is the total interest paid on an account over a 365-day period, taken from the interest rate and the frequency of compounding (12 CFR 1030.2)¹. The annual percentage rate, or APR, is a measure of the cost of credit, expressed as a yearly rate (12 CFR 1026.22)⁴. One term covers what a deposit earns, and the other covers what a loan costs.

The word “rate” hides a second difference. The interest rate on a deposit account is the annual rate of interest paid on the account which does not reflect compounding¹. On the disclosure forms for deposits, that rate may also be called the “annual percentage rate”¹. So APR is sometimes the label on a rate that has not been compounded yet, and APY is always the compounded version¹.

The APY formula, step by step

The textbook version is called the effective annual yield. It converts compound interest to its equivalent simple interest rate, so two accounts that compound on different schedules can be compared directly³. It is built on $1 invested for 1 year³.

1. Write the quoted rate as a decimal. A 6% rate is r = 0.06³.
2. Divide by the number of compounding periods in a year. The variable n is the number of times the interest is compounded in a year, 4 for quarterly, 12 for monthly, 365 for daily³.
3. Add 1, raise the sum to the power n, subtract 1. That is Y = (1 + r ÷ n)^n − 1, and Y is the equivalent annual simple interest rate³.
4. Multiply by 100 for percent. A rate of 6% compounded quarterly gives 1.015^4 − 1 = 0.0614, which is equivalent to a simple interest rate of 6.14%³.

Regulation DD uses a second form built from dollars instead of rates. The APY equals 100 times [(1 + Interest ÷ Principal) raised to 365 ÷ Days in term, minus 1], where Principal is the amount assumed deposited at the start and Interest is the total dollars earned on it over the term². For an account with no stated maturity, the term is assumed to be 365 days, and the calculation assumes all principal and interest stay on deposit with no other transactions².

Worked example (our arithmetic). The rule text works one case: $61.68 of interest on $1,000 over 365 days is an APY of 6.17%². Run backwards, our arithmetic shows a 6% rate compounded monthly pays exactly that:

The same bank can therefore call an account “6% interest” and “6.17% APY” in one sentence, and both are correct².

Try your own numbers

The defaults reproduce the 5% monthly case below³. Set the schedule to yearly and the APY drops back to the quoted rate³.

What is the difference between 5% APR and 5% APY?

For a deposit, the gap depends on how often interest is added. A 5% quoted rate has an APY of exactly 5.00% if interest is paid once a year, and a higher APY if interest is paid more often, because later interest is earned on earlier interest³¹⁰. Earning interest on principal and on interest over and over again is compound interest¹⁰.

Worked example (our arithmetic). Inputs: the quoted rates 5% and 24%, and the effective-yield formula³. The figure draws the same numbers.

At 5% the four schedules differ by 0.13 points, about $1.27 a year on $1,000 (our arithmetic)³. At 24% they differ by 3.11 points, about $31.15 a year on $1,000 (our arithmetic)³. Compounding matters more the higher the rate.

A smaller case has the same shape: 5% compounded daily is equivalent to earning 5.13% as simple interest³. And it shows why the schedule can swing a comparison. Three banks quote 2.08% compounded monthly, 2.09% compounded annually and 2.05% compounded daily³. The bank with the lowest headline rate is not the lowest earner, because the effective yields are 2.10%, 2.09% and 2.07% and the monthly account has the highest³.

What is 5% APY on $1,000 monthly?

A 5% APY already includes the monthly compounding, so $1,000 left for a year ends at $1,050.00 and has earned $50.00¹³. The monthly rate that produces it is slightly under 0.41%, and the stated rate before compounding is about 4.89% (our arithmetic)³.

Worked example (our arithmetic). Inputs: 5% APY, monthly steps, the effective-yield formula solved for the monthly rate i, which is 1.05^(1/12) − 1³.

The last row reads the question the other way: a $1,000 deposit every month rather than once. Interest of $272.58 on $12,000 is the compounding doing its work at the same 5% APY (our arithmetic)³.

APR vs interest rate

On a loan the two numbers diverge because of fees. The finance charge is the cost of consumer credit as a dollar amount, and it includes any charge payable directly or indirectly by the consumer and imposed by the creditor as an incident to or a condition of the extension of credit⁵. Interest is only the first item on its list; points, loan fees, appraisal and credit report fees, and similar charges follow it⁵. Fees charged by a mortgage broker are finance charges even when the lender does not require the consumer to use a broker⁵.

The APR then relates the amount and timing of value received by the consumer to the amount and timing of payments made⁴. It is worked out by the actuarial method in Appendix J of Regulation Z⁴. So two loans with the same interest rate can have different APRs, because the one with more upfront charges delivered less money for the same payments.

Worked example (our arithmetic). Inputs: a $10,000 loan, 12 equal monthly payments, a 6% interest rate; the payment is $860.66 from the loan payment formula (our arithmetic)⁴. We treat a $200 loan fee as a finance charge⁵ and solve for the monthly rate that makes the payments worth the $9,800 actually received, then multiply by 12 as the credit-card rule does⁴⁶.

A $200 fee on a $10,000 one-year loan adds 3.80 points to the APR (our arithmetic). The effect shrinks as the term lengthens, because the same fee is spread over more months of use. The disclosed APR is allowed some slack: it is accurate if it is within one-eighth of a percentage point above or below the figure determined by the rule, and one-quarter of a point for an irregular transaction⁴.

How credit card APR works

A card’s APR is not compounded in the disclosure. Where periodic rates are used to compute the finance charge, the APR to be disclosed is computed by multiplying each periodic rate by the number of periods in a year⁶. A daily periodic rate therefore becomes a daily rate times 365⁶. The effective cost of carrying a balance is higher than that quoted figure when interest is added to the balance, which is the same compounding gap as above³.

Worked example (our arithmetic). Inputs: a 24% APR, a $1,000 balance, no payments for a year, interest added back daily or monthly⁶³.

The “24% APR” label and the 27.11% effective figure describe the same card³. Late fees and penalties would come on top and are not in this arithmetic.

Is an APR of 24% good?

For a borrower, a lower APR means a lower cost of credit⁴. The Federal Reserve’s consumer credit release of October 7, 2026 puts the rate on credit card accounts assessed interest at 22.36% in the latest column, August 2026⁷. That figure is the annualized ratio of total finance charges at all reporting banks to the average daily balances they were charged on⁷. The all-accounts figure is a different measure: the stated APR averaged across all credit card accounts⁷. A 24% APR sits 1.64 points above that average of 22.36% (our arithmetic)⁷.

Is an APY of 3% good?

Compare it with what depositors earn on average. The national rate for savings was 0.38% as of October 19, 2026 (FDIC rate table), against 0.63% for money market accounts and 1.76% for 12-month CDs⁸. The national rate is the average of rates paid by all insured depository institutions and credit unions for which data is available, weighted by each institution’s share of domestic deposits⁸.

Worked example (our arithmetic). Inputs: $1,000 held for a year at each APY⁸¹.

At 3% APY the account earns about 7.9 times the national savings rate (our arithmetic)⁸. Whether that is “good” also depends on prices rising: the Federal Reserve judges inflation of 2 percent over the longer run, measured by the personal consumption expenditures price index, as most consistent with its mandate⁹. A yield above that pace adds buying power, and one below it loses some, which is arithmetic and not a recommendation about any account⁹.

Reading an APY disclosure

Four rules in Regulation DD explain most surprises in an advertised APY.

• Bonuses mostly stay out. The APY does not include the value of a bonus worth $10 or less².
• Variable rates freeze. For a variable-rate account, the institution bases the calculation only on the initial rate in effect when the account is opened or advertised, and assumes it does not change².
• Steps are averaged. For a $1,000 six-month CD that pays 5% compounded daily for three months and 5.5% for the next three, total interest is $26.68 and the APY is 5.39%².
• Tiers get their own APY. An APY, or a range, must be disclosed for each balance tier².

Compare APY with APY and APR with APR. A deposit rate quoted as an interest rate is not compounded¹, and the same words on a loan include fees⁵. For the formulas that sit behind a year of compounding, see the compound interest formula; for a rough doubling time, the Rule of 72; and for how a loan’s payment and APR play out over its term, how long it takes to pay off a loan.