APY vs APR Explained: Understanding the Two Most Important Interest Rates

Clear Definitions: What APY and APR Actually Mean

Before diving into formulas and comparisons, let's establish crystal-clear definitions of these two fundamental financial terms. Understanding their precise meanings is the first step to making smarter decisions about your money.

APR: Annual Percentage Rate

APR (Annual Percentage Rate) is the annualized cost of borrowing money expressed as a percentage, calculated without accounting for compounding within the year. It represents the nominal or stated interest rate that financial institutions use to describe loan costs. When a lender quotes you "18% APR," they are telling you the yearly rate before any compounding effects are applied. According to the Consumer Financial Protection Bureau (CFPB), APR must be disclosed on all consumer credit products under federal law.

Think of APR as the "sticker price" of borrowing. Just as a car's sticker price doesn't include taxes, registration, and dealer fees, APR doesn't include the additional cost created when interest compounds on itself throughout the year. For mortgages specifically, APR does include certain fees like origination charges and points, making it a more comprehensive measure than the base interest rate alone.

APY: Annual Percentage Yield

APY (Annual Percentage Yield) is the total return you earn on a deposit over one year, expressed as a percentage, with compounding fully accounted for. When a bank advertises "5.00% APY" on a savings account, that number represents exactly what you'll earn if you leave your money untouched for a full year. The FDIC requires all depository institutions to disclose APY under the Truth in Savings Act.

Think of APY as the "out-the-door price" of earning interest. It tells you the actual, effective return after all compounding benefits are included. No additional math required. If Bank A offers 5.00% APY and Bank B offers 4.95% APY, Bank A definitively pays more — the comparison is direct and complete.

The One-Sentence Difference

Here's the simplest way to remember: APR is the rate before compounding; APY is the rate after compounding. For any given nominal rate with compounding more frequent than annual, APY will always be higher than APR.

What Is APR (Annual Percentage Rate)?

APR stands for Annual Percentage Rate. It represents the annual cost of borrowing money or, less commonly, the annual rate of return on an investment, expressed as a percentage. The critical characteristic of APR is that it does not account for compounding within the year. It is a simple, annualized rate.

When a credit card company advertises a 24% APR, they mean the nominal annual rate is 24%. However, because credit card interest typically compounds daily, the actual cost of carrying a balance for one full year is higher than 24%. The APR tells you the rate before compounding effects are applied.

How APR Is Calculated

For most consumer loans, APR is calculated by taking the periodic interest rate and multiplying it by the number of periods in a year:

For example, if a credit card charges 2% per month, the APR is 2% × 12 = 24%. For mortgages, APR also includes certain fees and closing costs, making it a broader measure of borrowing cost than the base interest rate alone. The Consumer Financial Protection Bureau (CFPB) requires lenders to disclose the APR on all consumer loans under the Truth in Lending Act (TILA), so borrowers can compare the true cost of different loan offers on a standardized basis.

Where APR Is Used

• Credit cards: All credit card offers display an APR (often a range such as 19.99% – 29.99% depending on creditworthiness)
• Mortgages: Lenders quote both the base interest rate and the APR, which includes origination fees, points, and other costs
• Auto loans: Dealerships and banks advertise the APR on car financing
• Personal loans: Online lenders and banks express personal loan costs as APR
• Student loans: Both federal and private student loans are quoted in APR

In every borrowing context, the APR is the standard disclosure metric because it provides a consistent way to compare loan products, even when they have different fee structures or compounding schedules.

What Is APY (Annual Percentage Yield)?

APY stands for Annual Percentage Yield. It represents the total amount of interest you earn on a deposit over one year, including the effect of compounding. APY gives you a more accurate picture of your actual earnings than a simple stated rate because it factors in how often interest is calculated and added to your balance.

When a savings account advertises a 5.00% APY, that number already includes the compounding benefit. You do not need to do any additional math to understand your effective annual return — the APY is your effective annual return.

The APY Formula

APY is derived directly from the compound interest formula. It calculates the effective annual rate by compounding the periodic rate over all periods in one year:

Where:

• r = the nominal annual interest rate (APR) expressed as a decimal
• n = the number of compounding periods per year

Step-by-Step APY Calculation

Suppose a certificate of deposit has a stated rate of 5.00% with daily compounding. Here is how to find the APY:

The 5.00% stated rate produces an effective annual yield of 5.127% when compounded daily. On a $50,000 deposit, that 0.127% difference amounts to an extra $63.50 in earnings per year. Over 10 years without withdrawals, the difference compounds further.

Where APY Is Used

• Savings accounts: Banks are required by law to display APY under the Truth in Savings Act (Regulation DD), enforced by the FDIC
• Certificates of deposit (CDs): APY allows direct comparison across CDs with different compounding frequencies
• Money market accounts: APY reflects the actual yield you receive
• Some investment products: Bond yields and certain fixed-income instruments may be quoted as APY

The Mathematical Relationship Between APR and APY

Understanding the mathematical connection between APR and APY helps demystify why these numbers differ and by how much. The relationship is governed by a precise formula rooted in compound interest mathematics.

The Core Equation

The relationship between APR and APY depends entirely on the compounding frequency (n). The formula that connects them is:

This formula reveals several important mathematical truths:

• When n = 1 (annual compounding): APY = (1 + APR/1)^1 - 1 = APR. The rates are identical.
• When n > 1: APY > APR. The more frequent the compounding, the greater the gap.
• As n approaches infinity (continuous compounding): APY = e^APR - 1, where e is Euler's number (approximately 2.71828).

Why APY Is Always Greater Than or Equal to APR

The mathematical reason APY can never be less than APR lies in the nature of exponential growth. When interest compounds, you earn interest on previously earned interest. This creates a multiplying effect that always adds to the base return. Consider a 6% APR:

• With annual compounding (n=1): You earn 6% once at year's end. APY = 6.000%
• With monthly compounding (n=12): You earn 0.5% monthly, but each month's interest earns its own interest. APY = 6.168%
• With daily compounding (n=365): You earn 0.0164% daily, compounding 365 times. APY = 6.183%

The Federal Reserve publishes research on interest rate mechanics that confirms this mathematical relationship holds universally across all positive interest rates and compounding frequencies.

The Convergence Toward Continuous Compounding

An interesting mathematical property: as compounding frequency increases, the APY approaches a limit defined by continuous compounding. For a 5% APR:

• Monthly (n=12): APY = 5.116%
• Daily (n=365): APY = 5.127%
• Hourly (n=8,760): APY = 5.127%
• Continuous (n=∞): APY = 5.127% (e^0.05 - 1)

Notice that daily compounding captures almost all the benefit of continuous compounding. This is why most banks settle on daily compounding for savings products — more frequent compounding provides negligible additional benefit while adding computational complexity.

APY vs APR: Side-by-Side Comparison

The following table summarizes the fundamental differences between APY and APR:

A simple rule of thumb: when you are the one paying interest (loans, credit cards), pay attention to APR. When you are the one earning interest (savings, CDs), pay attention to APY. Lenders prefer to advertise APR because the number looks lower. Banks prefer to advertise APY because the number looks higher. Both practices are entirely legal and, in fact, required by their respective regulations.

When Each Rate Is Used: Savings vs Loans

Financial institutions don't randomly choose between APR and APY. Federal regulations dictate which rate must be displayed for which products. Understanding these rules helps you know what to look for and why.

Products That Display APY (You're Earning Interest)

Under the Truth in Savings Act (Regulation DD), depository institutions must disclose APY for:

• Savings accounts: Traditional savings, high-yield savings, and online savings accounts all display APY
• Certificates of deposit (CDs): Whether 6-month, 1-year, or 5-year CDs, the rate shown is APY
• Money market accounts: These hybrid checking-savings products display APY
• Interest-bearing checking: Reward checking accounts show their earnings as APY

The reasoning: when you deposit money, you want to know exactly what you'll earn. APY provides that certainty by including all compounding effects.

Products That Display APR (You're Paying Interest)

Under the Truth in Lending Act (TILA/Regulation Z), lenders must disclose APR for:

• Credit cards: Both purchase APR and cash advance APR are shown as APR
• Mortgages: The mortgage APR includes interest plus certain closing costs
• Auto loans: Dealership financing and bank auto loans show APR
• Personal loans: Unsecured personal loans from banks or online lenders display APR
• Student loans: Federal and private student loan rates are expressed as APR
• Home equity lines of credit (HELOCs): These variable-rate products display APR

The reasoning: APR provides a standardized way to compare borrowing costs across products with different fee structures. For mortgages specifically, APR helps borrowers compare loans even when one has higher fees but a lower rate.

Why This Distinction Matters

Consider this scenario: You see a savings account advertising "4.75%" and a credit card displaying "22%." Are these comparable? No. The savings rate is likely APY (what you'll actually earn), while the credit card rate is APR (before daily compounding adds to your cost). The true effective rate on that credit card is approximately 24.6% APY. Understanding which metric each product uses prevents costly misunderstandings.

How Compounding Frequency Turns APR into Different APY Values

The same nominal APR produces different APY values depending on how often interest compounds. More frequent compounding means your interest starts earning its own interest sooner, resulting in a higher effective yield. The table below shows this relationship across multiple rates and frequencies. For a deeper analysis, see our compounding frequency comparison guide.

Several patterns emerge from this data. First, when compounding is annual (n=1), APY equals APR exactly because there is no within-year compounding to create additional growth. Second, the gap between APR and APY is modest at low rates: at 3% APR with daily compounding, APY is only 3.045%, a difference of 0.045 percentage points. Third, the gap becomes dramatic at high rates: a 24% APR (typical for credit cards) compounded daily produces an effective APY of 27.116%, meaning the true annual cost is over three full percentage points higher than the advertised rate.

This is precisely why understanding the distinction matters. If you carry a credit card balance at a "24% APR" and interest compounds daily, you are effectively paying 27.12% per year on your debt. Use our compound interest calculator to see the real cost over any time period.

Which Financial Products Use Which Rate?

This comprehensive table shows which rate type is displayed for common financial products, helping you understand what you're actually looking at when comparing offers.

Notice the pattern: products where you earn money show APY; products where you pay money show APR. This is not coincidental — it's by regulatory design to ensure consumers see the most relevant number for their situation. Banks and the FDIC enforce these disclosure requirements strictly.

When APR Matters More: Borrowing Decisions

APR is the rate to focus on whenever you are taking on debt. Federal law under the Truth in Lending Act requires lenders to disclose APR so consumers can make apples-to-apples comparisons across loan products.

Credit Cards

Credit card APRs typically range from 19% to 29% as of early 2026. Because credit card interest compounds daily on outstanding balances, the effective cost (APY) is significantly higher than the stated APR. A card with a 22% APR actually costs approximately 24.60% APY. If you carry a $10,000 balance for a full year, you would owe roughly $2,460 in interest rather than the $2,200 the APR alone might suggest — a difference of $260.

According to the Federal Reserve's G.19 consumer credit report, the average credit card interest rate has consistently exceeded 20% in recent years. This makes understanding the compounding effect on credit card debt especially important.

Mortgages

Mortgage APR is unique because it includes not just the interest rate but also origination fees, discount points, mortgage insurance, and certain closing costs. Two mortgage offers with the same base interest rate can have different APRs if their fee structures differ. The APR gives you a more complete picture of total borrowing cost. However, because most mortgages compound monthly (not daily), the difference between the stated rate and the effective rate due to compounding alone is relatively small.

Auto Loans and Personal Loans

Auto loans and personal loans are typically quoted at a fixed APR. Because these are amortizing loans with set monthly payments, the compounding effect is built into the payment schedule. When comparing two auto loan offers, the one with the lower APR will always cost less in total interest, assuming the same loan term and amount.

Why Lenders Prefer to Show APR

Lenders display APR because it is the legally required metric and because it produces a lower number than APY would. A credit card advertising "24% APR" sounds less alarming than "27.12% effective annual rate." While lenders are not hiding anything — APR is the mandated disclosure standard — borrowers benefit from understanding that the actual annual cost of their debt may be higher than the APR suggests.

When APY Matters More: Saving and Investing Decisions

APY is the rate to focus on whenever you are earning interest on your money. The Truth in Savings Act (Regulation DD) requires banks and credit unions to disclose APY on all deposit products, ensuring consumers can compare the actual yield across different accounts.

High-Yield Savings Accounts

When you shop for a savings account, APY is the only number you need to compare. Two banks might both offer a "4.75% rate," but if one compounds daily and the other compounds monthly, their APYs differ. The daily-compounding account produces a slightly higher effective yield. In practice, most online high-yield savings accounts already compound daily and advertise the resulting APY, so the number you see is the number you get.

Certificates of Deposit

Certificates of deposit are another area where APY is essential for comparison. A 12-month CD at Bank A with 5.10% APY will earn you more than a 12-month CD at Bank B with 5.05% APY, regardless of their underlying compounding frequencies. The APY has already normalized the compounding effect, making the comparison straightforward.

The Truth in Savings Act

The Truth in Savings Act, implemented through the FDIC's Regulation DD, specifically mandates that depository institutions:

• Disclose the APY on all deposit accounts
• Use a standardized formula to calculate APY, ensuring consistency across institutions
• Include the APY in all advertising that mentions a rate of return
• Provide APY information before the account is opened

This regulation exists precisely because comparing savings products using different stated rates and compounding frequencies would be confusing for consumers. APY solves this by giving everyone the same standardized effective rate.

Why Banks Prefer to Show APY

Banks display APY because it is legally required for deposit products and because it produces a higher number than the underlying APR. A savings account with a 4.85% nominal rate compounded daily has an APY of 4.969%. Advertising "4.97% APY" is more attractive than "4.85% rate." Again, nothing is being concealed — the APY accurately reflects what you will earn. Banks simply benefit from the more appealing number, just as lenders benefit from the lower APR number on loans.

How to Convert APR to APY: Step-by-Step Guide

Converting APR to APY is a straightforward calculation once you know the compounding frequency. This skill is particularly valuable when you want to understand the true cost of a loan or compare products where one shows APR and another shows APY.

The Conversion Formula

Where APR is expressed as a decimal (e.g., 5% = 0.05) and n is the number of compounding periods per year.

Common Compounding Frequencies

• Daily (n = 365): Most savings accounts, credit cards
• Monthly (n = 12): Many CDs, mortgages, auto loans
• Quarterly (n = 4): Some bonds, older savings accounts
• Semi-annually (n = 2): I Bonds, some corporate bonds
• Annually (n = 1): Some CDs, certain international accounts

Worked Example: Credit Card APR to True Cost

Your credit card has a 21.99% APR with daily compounding. What's the true annual cost?

Your "21.99% APR" credit card actually costs 24.57% per year when you carry a balance. On a $5,000 balance, that's $1,228.65 in annual interest versus the $1,099.50 you might expect from the APR alone — an extra $129.15.

Quick Reference: APR to APY Conversion Table

Use this table for quick conversions at common credit card and savings rates with daily compounding (n=365):

The pattern is clear: higher APRs produce exponentially larger gaps between APR and APY. At 30% APR, the effective rate is nearly 35% — almost five percentage points higher than advertised.

How to Convert Between APR and APY

Converting between these two rates requires the compound interest formula. The conversion depends on the compounding frequency (n).

Converting APR to APY

Example 1: Credit Card with 22% APR, Daily Compounding

The effective annual cost of this credit card debt is 24.60%, not 22%. On a $5,000 balance, that is $1,230 per year versus $1,100 — an additional $130 due purely to the compounding effect.

Example 2: Savings Account with 4.75% APR, Daily Compounding

A 4.75% nominal rate with daily compounding yields an effective 4.864% APY.

Converting APY to APR

To go in the other direction — extracting the nominal rate from a known APY — rearrange the formula:

Example 3: What APR Produces a 5.00% APY with Monthly Compounding?

To achieve a 5.00% APY with monthly compounding, the underlying nominal rate (APR) needs to be approximately 4.889%. The remaining 0.111 percentage points come from the compounding effect over twelve months.

Dollar Impact on a $100,000 Deposit

The following table illustrates the real-dollar difference between APR and APY on a $100,000 deposit held for one year at various rates with daily compounding:

At a 5% rate on $100,000, compounding adds $126.75 in a single year. While that may seem modest, remember that this extra amount compounds in subsequent years as well. Over 10 years with no withdrawals, the cumulative effect of compound interest on a $100,000 deposit at 5% daily compounding produces $64,866.47 in total interest, compared to $50,000 from simple interest alone — a difference of $14,866.47.

Why This Distinction Matters for Your Wallet

Understanding the APY vs APR difference isn't just academic — it has real financial consequences. Here's why this knowledge directly impacts your bottom line.

The Hidden Cost of Credit Card Debt

The average American household with credit card debt carries approximately $6,500 in balances, according to Federal Reserve data. At the average credit card APR of 22%, most consumers think they're paying $1,430 in annual interest. But with daily compounding, the true cost (APY) is 24.6%, meaning actual interest charges are closer to $1,600 — an extra $170 per year that compounds if not paid down.

Over five years of carrying that balance, the APR-APY misunderstanding costs you over $850 in interest you didn't anticipate. For households with larger balances or multiple cards, this hidden cost multiplies significantly.

The Savings Account Advantage You're Missing

On the flip side, understanding APY helps you appreciate the full value of your savings. When a high-yield savings account offers 5.00% APY, that's your actual return, including the benefit of daily compounding. If you only looked at the underlying nominal rate (about 4.88% APR), you might undervalue the account.

More importantly, when comparing savings products, APY gives you an apples-to-apples comparison. A CD offering "5.10% rate with monthly compounding" versus "5.05% APY" requires calculation to compare properly. The second product clearly states what you'll earn; the first requires you to compute the APY (which works out to about 5.22%) to realize it's actually better.

Making Smarter Financial Decisions

Armed with this knowledge, you can:

• Compare loan offers fairly: Convert all rates to the same basis before choosing
• Understand true debt costs: Know that your credit card's actual cost exceeds its stated APR
• Maximize savings returns: Choose accounts with higher APY, not just higher "rates"
• Avoid marketing tricks: Recognize when institutions are using the more favorable number
• Plan more accurately: Use APY for projecting actual earnings, not the nominal rate

The Consumer Financial Protection Bureau provides additional resources for understanding interest rates and making informed financial decisions.

Common Mistakes When Comparing APY and APR

1. Comparing APR on Savings to APR on Loans

Some consumers see a savings account advertising "4.50%" and a credit card charging "22%" and calculate the net cost as 17.5%. But if the savings rate is APY and the credit card rate is APR (compounded daily to an effective 24.6%), the actual gap is wider. Always make sure you are comparing the same type of rate.

2. Ignoring Variable Rate Changes

Many high-yield savings accounts offer variable APYs that change when the Federal Reserve adjusts the federal funds rate. A 5.00% APY advertised today might drop to 4.25% in six months. CDs offer protection against this because they lock in a rate for a fixed term.

3. Overlooking Fees That Erode APY

An account with a 5.00% APY but a $10 monthly maintenance fee on a $2,000 balance effectively yields only 2.60% after fees. When evaluating savings products, subtract any recurring fees from your expected earnings to get the true net yield.

4. Assuming APR on a Mortgage Is the Full Cost

While mortgage APR includes many fees, it does not include all costs. Property taxes, homeowner's insurance, and private mortgage insurance (PMI) are excluded from APR but represent real costs of homeownership. APR is useful for comparing mortgage offers, but it understates the total expense of the loan.

5. Thinking Higher APY Always Means a Better Deal

A promotional 6-month CD with 5.50% APY sounds better than a 12-month CD at 5.10% APY, but if rates drop after six months, you may end up reinvesting at 4.00% when the short CD matures. Consider the full time horizon, not just the headline rate. The SEC's guide to saving and investing provides additional context on evaluating fixed-income yields.

Frequently Asked Questions