APR vs. APY vs. Interest Rate: What Each Number Tells You

Three rates show up on almost every financial product: the interest rate, the APR, and the APY. They look similar and often sit next to each other, but each answers a different question. The interest rate tells you what is charged or paid on a balance. The APR tells you the yearly cost of credit, including certain fees. The APY tells you what a deposit actually earns in a year once compounding is counted.

This guide explains each one, shows the federal rules behind them, and works through the math so you can check the numbers on any disclosure.

What is the difference between an interest rate, APR and APY?

The short answer: the interest rate is the base price, APR adds loan costs, and APY adds compounding.

The direction of the effect is predictable. On a loan with fees, the APR is higher than the interest rate. On a deposit that compounds more than once a year, the APY is higher than the interest rate. If a loan has no fees, or a deposit compounds only once a year, the numbers match.

What does APR measure on a loan?

APR measures the yearly cost of credit as a percentage, combining the interest rate with certain prepaid finance charges such as origination fees. It answers: “If I spread every finance cost evenly over the loan, what yearly rate am I really paying?”

Truth in Lending: why APR exists

The Truth in Lending Act, implemented by Regulation Z, requires lenders to disclose the APR along with the finance charge, the amount financed and the total of payments for closed-end loans. Credit card agreements must list each APR (purchase, balance transfer, cash advance, penalty) and the fees. The goal is a common yardstick, so a loan with a lower rate but a large fee does not look cheaper than it is.

Regulation Z also sets an accuracy tolerance. For most standard loans, a disclosed APR counts as accurate if it is within 1/8 of 1 percentage point of the true figure; for irregular transactions, the tolerance is 1/4 of 1 percentage point.

Worked example: how a fee raises the APR

Say you are offered a $20,000 personal loan at a 7.00% interest rate for 60 months, with a $500 origination fee taken out of the proceeds. Assume monthly payments at the end of each month.

1. Monthly rate: 7.00% ÷ 12 = 0.58333% (0.0058333).
2. Monthly payment: $20,000 × 0.0058333 ÷ (1 − 1.0058333^−60) = $396.02.
3. Total of payments: $396.02 × 60 = $23,761.20.
4. Interest alone: $23,761.20 − $20,000 = $3,761.20.
5. Amount financed (what you actually receive): $20,000 − $500 = $19,500.
6. Finance charge: interest plus the fee, $3,761.20 + $500 = $4,261.20.
7. APR: find the monthly rate at which 60 payments of $396.02 have a present value of $19,500. Solving numerically gives about 0.6723% per month, or 0.6723% × 12 = 8.07% APR.

So the same loan carries a 7.00% interest rate and an 8.07% APR. If a second lender offered 7.50% with no fee, its APR would be 7.50%, which is lower. That is exactly the comparison APR is designed to make visible. The loan comparison calculator and the total cost of loan calculator let you run your own offers.

What APR leaves out

APR is useful, but it has limits:

• It does not include compounding. APR is a periodic rate times the number of periods in a year.
• It does not include every cost. Some charges, such as certain third-party or late fees, are excluded from the finance charge.
• It assumes you keep the loan to the end. Fees spread over 60 months raise the APR modestly; if you pay off in 12 months, your real cost per year is higher.
• On variable-rate credit, it can change. A card’s APR can move with an index.

What does APY measure on a savings account?

APY measures what a deposit earns in a year, including the effect of compound interest. It answers: “If I leave $1 here for a year, how much will I have earned?”

Truth in Savings: why APY exists

The Truth in Savings Act, implemented by Regulation DD, requires banks and savings institutions to disclose the APY, the interest rate, the compounding frequency and crediting schedule, the balance method, minimum balances, fees and, for CDs, the term and early-withdrawal penalty. Advertisements that state a rate of return generally must state it as an APY. Credit unions follow parallel rules under their own federal regulator.

For an account with a one-year term, Regulation DD’s formula boils down to:

APY = 100 × [(1 + Interest ÷ Principal)^(365 ÷ Days in term) − 1]

For a year-long term, that is simply interest earned divided by principal.

Worked example: rate vs. APY

Say one account pays a 4.50% interest rate compounded daily and another pays 4.40% compounded monthly. You deposit $10,000 in each for one year.

Account 1 (4.50%, daily):

1. Daily rate: 0.045 ÷ 365 = 0.00012329.
2. Growth over 365 days: (1.00012329)^365 = 1.046025.
3. Interest: $10,000 × 0.046025 = $460.25.
4. APY: $460.25 ÷ $10,000 = 4.60%.

Account 2 (4.40%, monthly):

1. Monthly rate: 0.044 ÷ 12 = 0.0036667.
2. Growth over 12 months: (1.0036667)^12 = 1.044898.
3. Interest: $10,000 × 0.044898 = $448.98.
4. APY: 4.49%.

The APY makes the comparison immediate: 4.60% beats 4.49%, and the difference on $10,000 is $11.27 a year. These are illustrative rates, not current market figures. The compare CD rates calculator and the CD calculator apply the same idea to time deposits.

How much does compounding frequency add?

Less than most people expect. Here is what a 5.00% nominal rate becomes at different compounding schedules:

The jump from annual to monthly is about 0.12 percentage point; from monthly to daily, about 0.01. The compounding frequency calculator lets you test other rates and schedules.

Why does a credit card APR understate the yearly cost?

A credit card APR understates the cost of a balance carried all year because it does not include compounding. The APR is the periodic rate multiplied by the number of periods, while the issuer actually adds interest to your balance as it goes.

Say your card charges 24% APR and, to keep it simple, interest compounds monthly:

1. Monthly periodic rate: 24% ÷ 12 = 2%.
2. Effective annual rate: (1.02)^12 − 1 = 0.26824.
3. Effective cost: about 26.82% a year, not 24%.

With daily compounding the effective rate is slightly higher still. This gap only matters if you carry a balance; if you pay the statement balance in full by the due date, the grace period on most cards means you pay no purchase interest at all. The credit card payoff calculator shows what a carried balance costs in dollars.

How do you convert between a rate, APR and APY?

You convert a nominal rate to an effective yearly rate with one formula, and you can run it backward when you only know the APY.

• Rate to APY: APY = (1 + rate ÷ n)^n − 1, where n is compounding periods per year.
• APY to rate: rate = n × [(1 + APY)^(1 ÷ n) − 1].

Take the 4.60% APY account from the earlier example, which compounds daily. Working backward: 365 × [(1.046025)^(1 ÷ 365) − 1] = 0.0450, or 4.50%, which is the stated rate. If the same 4.60% APY came from monthly compounding instead, the underlying rate would be 12 × [(1.046025)^(1 ÷ 12) − 1] = about 4.51%.

For a credit card, the conversion that matters is APR to daily periodic rate. A 24% APR divided by 365 is a daily rate of about 0.0658%. If that rate compounded every day for a full year on an unchanged balance, the effective annual cost would be (1 + 0.24 ÷ 365)^365 − 1, or about 27.11%, a bit higher than the 26.82% from monthly compounding.

One caution: converting a loan APR into an effective rate does not remove the fees baked into it. If you want the effective cost of interest alone, start from the note rate, not the APR.

Variable rates and promotional rates

Both APR and APY describe a moment in time when the rate can change. A variable-rate card’s APR moves with an index; a savings account’s APY can change whenever the institution adjusts its rate. Promotional rates add a second layer: a 0% introductory APR or a bonus APY applies only for a stated period. Truth in Lending and Truth in Savings disclosures must tell you how long a promotional rate lasts and what rate applies afterward, so read the “after” number as carefully as the headline.

When should you use each number?

Use each number for the job it was built for:

• Shopping for a loan: compare APRs for the same term and loan type. Then check the total of payments, because a longer term with a lower APR can still cost more dollars.
• Shopping for a savings account or CD: compare APYs for the same term, then read the fees, minimum balance and penalty terms.
• Figuring next month’s interest: use the interest rate (or the periodic rate on a card statement), not the APR or APY.
• Deciding between paying debt and saving: convert both to effective annual rates before comparing, and remember that savings interest is generally taxable.

Common mix-ups

• Comparing a loan’s interest rate to another loan’s APR. One includes fees and one does not.
• Treating a high APY as a guarantee. On a variable-rate account, the rate can change after you open it; the disclosure tells you whether and how.
• Assuming APR equals the effective cost of a card. It does not include compounding.
• Ignoring the term. A promotional APY that lasts three months is not the same as a fixed APY on a 12-month CD.

Bottom line

The interest rate is the raw price. APR is the borrowing yardstick required by Truth in Lending: it adds certain fees but not compounding. APY is the savings yardstick required by Truth in Savings: it adds compounding. Compare loans by APR, compare deposits by APY, and when you need to compare across the two, convert both to an effective annual rate and look at total dollars over your actual time frame.