What is the difference between APR and APY?

APR (Annual Percentage Rate) and APY (Annual Percentage Yield) both measure interest rates, but APR is a simple interest rate while APY accounts for compound interest. The key difference: APR = Nominal rate (simple interest without compounding). Used for loans, credit cards (stated rate), and borrowing costs. Formula: Simple interest = Principal × Rate × Time. APY = Effective rate (includes compound interest). Used for savings accounts, CDs, and investment returns. Formula: APY = (1 + r/n)^n - 1, where r=APR and n=compounding periods. Real-world example: 5% APR with daily compounding = 5.127% APY. On $10,000, APR suggests $500 interest, but APY shows you actually earn $512.70 due to compounding. The more frequent the compounding, the larger the gap between APR and APY. Daily compounding (365x/year) yields higher APY than monthly (12x/year) or annual (1x/year). For borrowers: Higher compounding frequency means paying more interest than APR suggests. Credit cards state 18% APR but with daily compounding, effective APY is 19.72%. For savers: Higher compounding means earning more than APR suggests. 4% APR with daily compounding = 4.081% APY. Bottom line: APY is always the true rate - what you actually earn or pay after accounting for compounding.

How do you convert APR to APY?

Converting APR to APY requires knowing the compounding frequency. The formula is: APY = (1 + r/n)^n - 1, where r = APR as decimal (5% = 0.05) and n = number of compounding periods per year. Compounding frequencies: Daily (n=365), Monthly (n=12), Quarterly (n=4), Semi-annually (n=2), Annually (n=1, APY = APR). Step-by-step example: Convert 6% APR with monthly compounding to APY. APR = 6% = 0.06, n = 12 (monthly). APY = (1 + 0.06/12)^12 - 1 = (1 + 0.005)^12 - 1 = (1.005)^12 - 1 = 1.06168 - 1 = 0.06168 = 6.168%. Result: 6% APR with monthly compounding = 6.168% APY. Same APR with different compounding: 6% APR daily = 6.183% APY (highest), 6% APR monthly = 6.168% APY, 6% APR quarterly = 6.136% APY, 6% APR semi-annually = 6.09% APY, 6% APR annually = 6.000% APY (lowest). Key insight: More frequent compounding = higher APY. The difference seems small but compounds significantly over time. For $100,000 at 6% APR: Daily compounding earns $6,183, Annual compounding earns $6,000, Difference = $183 extra per year from daily vs annual compounding. Use our calculator to instantly convert any APR to APY with your specific compounding frequency.

Why do banks advertise APY instead of APR for savings accounts?

Banks advertise APY for savings accounts because it's legally required and shows a higher, more attractive number than APR. Regulation DD (Truth in Savings Act) mandates that banks disclose APY, not just APR, for deposit accounts. This ensures transparency about actual earnings including compound interest. Why APY is higher and more appealing: 4.50% APR with daily compounding = 4.60% APY. The 0.10% difference seems small but matters on large balances. On $50,000, that's $50 extra per year. Banks benefit from showing the higher APY number in marketing. "Earn 4.60% APY!" looks better than "Earn 4.50% APR!" Consumers benefit because APY reflects true earnings, not understated simple interest. Real comparison example: Savings account advertised as "4.50% APY": Actual APR is ~4.40%, Daily compounding brings effective yield to 4.50%. You earn based on APY (4.50%), not APR (4.40%). On $25,000 = $1,125/year, not $1,100. Extra $25 from compounding. Historical context: Before Truth in Savings Act (1991), banks could advertise misleading rates. Some showed simple interest rates that didn't reflect compounding. Consumers couldn't accurately compare accounts. APY standardization enabled "apples to apples" comparison. Important: When comparing savings accounts, ALWAYS use APY, not APR. APY accounts for all compounding effects and gives true earning power. Ignore APR entirely for savings - APY is the only number that matters. For loans and credit cards, the opposite is true - APR is standard (though APY would show true cost with compounding).

Does compounding frequency really make a big difference?

Yes, compounding frequency makes a measurable difference, especially over time and with larger balances. The impact increases with higher rates and longer timeframes. Annual impact example (5% APR on $10,000): Daily compounding (365x) = 5.127% APY = $512.70 earned, Monthly compounding (12x) = 5.116% APY = $511.60 earned, Quarterly compounding (4x) = 5.095% APY = $509.50 earned, Annual compounding (1x) = 5.000% APY = $500.00 earned, Difference (daily vs annual) = $12.70 per year (2.54% more earnings). Larger balance impact ($100,000 at 5% APR): Daily compounding earns $5,127, Annual compounding earns $5,000, Difference = $127 per year. Over 10 years = $1,270+ extra from daily compounding. Higher rate impact (10% APR on $10,000): Daily compounding = 10.516% APY = $1,051.60, Annual compounding = 10.000% APY = $1,000.00, Difference = $51.60 per year (5.16% more). Long-term compounding power (20 years, $10,000 at 6% APR): Daily compounding (6.183% APY) = $33,200 final value, Annual compounding (6.000% APY) = $32,070 final value, Difference = $1,130 extra from daily compounding! When it matters most: High-yield savings accounts (4-5% APY) - daily vs monthly compounding adds $20-40 per $10,000 annually. Credit card debt (18-25% APR) - daily compounding costs significantly more than stated APR suggests. Large investment accounts - even 0.1% APY difference on $500,000 = $500/year. When it matters less: Low rates (under 1%) - minimal practical difference. Small balances (under $1,000) - difference measured in cents. Short timeframes (under 1 year) - compounding hasn't had time to work. Bottom line: Compounding frequency becomes increasingly important with higher rates, larger balances, and longer timeframes. Always choose daily compounding for savings when available.

What does APY mean on a savings account?

APY (Annual Percentage Yield) on a savings account is the total amount of interest you'll earn in one year, expressed as a percentage of your balance, including the effect of compound interest. It's the true rate of return on your savings. How APY works: APY includes compound interest (interest earned on interest), reflects how often interest compounds (usually daily or monthly), accounts for reinvested interest that itself earns interest, and represents actual annual earnings if balance and rate stay constant. Real example: Savings account with $5,000 and 4.50% APY with daily compounding: Month 1: Earn ~$18.75, balance = $5,018.75, Month 2: Earn ~$18.82 (slightly more because balance is higher), Month 3: Interest continues growing on increasing balance, Year total: Earn $225 (4.50% of $5,000), not $224.79 (4.487% without compounding). The 4.50% APY accurately predicts this $225 earning. Key characteristics: APY > APR (unless annual compounding, then equal). Higher APY = better return for savers. Standardized by law (Truth in Savings Act) for easy comparison. Assumes interest stays in account (compounds). Assumes rate doesn't change during year. What affects APY: Interest rate (base APR), compounding frequency (daily best), and minimum balance requirements (some accounts require $X to earn stated APY). Common savings account APYs (2024): Traditional banks: 0.01-0.50% APY (very low), High-yield online savings: 4.00-5.50% APY (excellent), Money market accounts: 3.50-5.00% APY (competitive), CDs: 4.00-5.50% APY (varies by term). How to use APY: Compare savings accounts using APY only (ignore APR). Calculate expected earnings: Balance × APY = Annual Interest. Verify actual interest matches APY (should be within pennies). Higher APY always means more money in your pocket when comparing similar accounts.

Is APR or APY better for comparing loans?

APR is the standard metric for comparing loans, but understanding APY reveals the true cost when interest compounds. Both matter, but serve different purposes. APR for loans (standard comparison metric): Includes interest rate plus most fees (origination fees, closing costs, mortgage insurance). Standardized by Truth in Lending Act for consumer loans. Enables "apples to apples" comparison between lenders. Represents cost as if simple interest (no compounding). Example: 6% APR mortgage with $5,000 fees might be effectively 6.25% APR. APY for loans (true cost with compounding): Accounts for how often interest compounds (monthly, daily). Shows actual cost you'll pay if making only required payments. Credit cards compound daily, making effective APY higher than stated APR. Example: 18% APR credit card with daily compounding = 19.72% effective APY. Real loan comparison example: Loan A: 5.50% APR, $800 fees, monthly compounding = 5.64% effective APY. Loan B: 5.75% APR, $200 fees, monthly compounding = 5.90% effective APY. APR comparison: Loan A looks better (5.50% vs 5.75%). But Loan A has higher fees: $800 vs $200. APY reveals true cost including fees and compounding. When APR is enough: Comparing similar loan products (e.g., two mortgages), both have similar compounding (typically monthly), focus on APR which includes fees. When to calculate APY: Credit cards (daily compounding makes huge difference), payday loans or short-term loans (compounding compounds quickly), comparing loan to savings opportunity cost, calculating true cost of debt. Why credit cards show APR not APY: Not legally required to show APY (unlike savings accounts). Stated APR looks lower and more appealing. Daily compounding makes APY much higher. Example: 24% APR = 27.03% APY with daily compounding. Best practice: Use APR for initial loan comparison (standardized), but calculate or check APY for true cost, especially with high-interest debt. For savings vs debt decisions, convert all rates to APY for accurate comparison.

How does daily compounding work?

Daily compounding means interest is calculated and added to your balance every single day (365 times per year), and each day's interest earns interest the next day. This creates a compounding snowball effect. How daily compounding calculation works: Day 1: Interest = Balance × (APR ÷ 365). This interest is added to balance. Day 2: Interest = New Balance × (APR ÷ 365). Slightly higher because balance increased. Day 3: Interest continues growing on ever-increasing balance. This repeats for 365 days. Real example ($10,000 at 5% APR with daily compounding): Day 1: Interest = $10,000 × (0.05 ÷ 365) = $1.3699. New balance = $10,001.37. Day 2: Interest = $10,001.37 × (0.05 ÷ 365) = $1.3701. New balance = $10,002.74. Day 30: Balance has grown to $10,041.10 (vs $10,041.67 with continuous compounding). Day 365: Final balance = $10,512.67. Total interest = $512.67 vs $500 with simple interest (annual compounding). Extra $12.67 from compounding effect. The compounding formula: Daily: A = P(1 + r/365)^365. For our example: $10,000(1 + 0.05/365)^365 = $10,512.67. Effective APY = 5.127% (vs 5.00% APR). Daily vs other compounding frequencies ($10,000 at 5% APR for 1 year): Daily (365x): $512.67 interest, 5.127% APY (best for savers). Monthly (12x): $511.62 interest, 5.116% APY. Quarterly (4x): $509.45 interest, 5.095% APY. Semi-annually (2x): $506.25 interest, 5.063% APY. Annually (1x): $500.00 interest, 5.000% APY (worst for savers). Why daily compounding matters: For savers: Maximizes returns - choose daily over monthly when possible. Difference grows with balance and rate: $100K at 5% APR = $127/year extra vs annual compounding. For borrowers: Increases true cost - credit card APR understates real cost. 18% APR = 19.72% APY with daily compounding costs extra $172/year on $10K balance. Where daily compounding appears: High-yield savings accounts (most compound daily), money market accounts, credit cards (works against you!), some investment accounts, and online banks (typically offer daily). Note: Some banks compound daily but only post interest monthly. Effect is same as daily, but you see balance change monthly, not daily.

Can APY be higher than the interest rate?

Yes! APY is almost always higher than the stated interest rate (APR) unless compounding happens only annually. This is because APY includes the effect of compound interest while APR does not. Why APY > APR (in most cases): APR is the nominal (stated) rate without compounding. APY includes compound interest (interest on interest). The more frequent the compounding, the higher APY rises above APR. With annual compounding, APY = APR (no additional compounding). Examples showing APY > Interest Rate: 5% interest rate (APR) with daily compounding = 5.127% APY. APY is 0.127% higher! 4% APR with monthly compounding = 4.074% APY (0.074% higher). 6% APR with quarterly compounding = 6.136% APY (0.136% higher). Extreme example - high rates with frequent compounding: 24% credit card APR with daily compounding = 27.03% APY! APY is 3.03% higher (12.6% more than stated rate). This is why credit cards are so expensive - you're paying APY, not APR. Mathematical reason: Compounding formula: APY = (1 + r/n)^n - 1. When n > 1 (any compounding more frequent than annual), the formula produces a result higher than r (the APR). Example: 5% APR, monthly compounding: APY = (1 + 0.05/12)^12 - 1 = 1.05116 - 1 = 0.05116 = 5.116% > 5.000% APR. Real-world implications: Savings account advertised as "4.50% APY" likely has ~4.40% APR. Credit card showing "18% APR" has ~19.72% effective APY (what you actually pay). CD at "5% APY" with daily compounding has ~4.879% APR. When APY = APR: Only when compounding is annual (once per year, n=1). Formula becomes: APY = (1 + r/1)^1 - 1 = r. No compound interest effect, so APY equals APR. Rare in modern banking - most accounts compound at least monthly. Why this matters: For savers: Always compare using APY, not APR. APY shows true earnings. Look for daily compounding to maximize returns. For borrowers: Stated APR understates true cost. Calculate APY to see what you're really paying. Credit cards cost 1-3% more than stated APR due to daily compounding. Bottom line: APY being higher than the stated rate is normal and expected - it's the compound interest effect working for savers (good) or against borrowers (bad).

APR vs APY Calculator - Annual Percentage Rate vs Yield | Compound Interest

APR vs APY: Understanding the Difference

APR (Annual Percentage Rate) and APY (Annual Percentage Yield) are both measures of interest rates, but they serve fundamentally different purposes. According to the FDIC, understanding this distinction is crucial for making informed financial decisions about savings and borrowing.

🔑 Key Distinction

APR = Simple annual rate (no compound interest)
APY = Effective annual rate (includes compound interest)
APY is ALWAYS the true rate you earn or pay!

What is APR (Annual Percentage Rate)?

APR is the nominal or stated annual interest rate without accounting for the effect of compound interest within the year. It represents simple interest as if it were calculated and paid once annually.

Where APR is used:

Credit cards: Stated APR on purchases (e.g., 18% APR)
Mortgages: Loan interest rate including some fees
Auto loans: Annual financing rate
Personal loans: Borrowing cost before compounding
Student loans: Interest rate disclosed to borrowers

APR formula (simple interest):

Interest = Principal × APR × Time

Example: $10,000 at 5% APR for 1 year = $10,000 × 0.05 × 1 = $500 interest

What is APY (Annual Percentage Yield)?

APY is the effective annual rate that accounts for compound interest. It shows what you actually earn or pay when interest compounds multiple times per year and you earn "interest on interest."

Where APY is used:

Savings accounts: Must disclose APY by law (Truth in Savings Act)
Money market accounts: True earnings with compounding
Certificates of Deposit (CDs): Actual yield over term
Investment returns: Real return with reinvestment
High-yield savings: Competitive rates with compounding

APY formula (compound interest):

APY = (1 + r/n)^n - 1

Where:
r = APR as decimal (5% = 0.05)
n = number of compounding periods per year

Example: 5% APR with monthly compounding
APY = (1 + 0.05/12)^12 - 1 = 1.05116 - 1 = 0.05116 = 5.116%

The Power of Compound Interest

Compounding frequency determines how much APY exceeds APR. The more frequently interest compounds, the higher your APY relative to APR.

Compounding Frequency	Times Per Year	5% APR → APY	$10,000 Earns
Daily	365	5.127%	$512.67
Monthly	12	5.116%	$511.62
Quarterly	4	5.095%	$509.45
Semi-annually	2	5.063%	$506.25
Annually	1	5.000%	$500.00

Key insight: Daily compounding earns $12.67 more per year than annual compounding on just $10,000. On $100,000, that's $126.70 extra annually - enough for a nice dinner each year just from compounding!

Real-World Applications

For Savers: Maximizing Returns

When comparing savings accounts, always use APY, not APR:

Savings Account Comparison

Account A: 4.40% APR, daily compounding = 4.50% APY
Account B: 4.45% APR, monthly compounding = 4.55% APY
Account C: 4.50% APR, quarterly compounding = 4.58% APY
Best choice: Account C (highest APY = most earnings)
On $25,000: Account C earns $1,145/year vs Account A's $1,125 = $20 extra

For Borrowers: Understanding True Cost

Credit cards state APR but charge interest with daily compounding, making the effective cost higher:

Credit Card True Cost

Stated rate: 18% APR (advertised)
Compounding: Daily (365 times per year)
True cost: 19.72% APY (what you actually pay)
On $5,000 balance:
APR suggests: $900/year interest
APY reality: $986/year interest
You pay $86 more than APR suggests!

When APY Matters Most

High-impact scenarios:

Large balances: Even 0.1% APY difference on $100,000 = $100/year
High interest rates: 10% APR compounds to 10.52% APY (daily) - 0.52% difference is significant
Long time periods: Compounding effect multiplies over years and decades
Credit card debt: Daily compounding makes stated APR very misleading
Investment comparisons: True return requires APY, not APR

Low-impact scenarios:

Low rates (under 1%): APR vs APY difference is minimal (pennies)
Small balances (under $1,000): Practical difference measured in cents
Short terms (under 1 year): Compounding hasn't had time to work
Annual compounding: APY = APR, no difference

Why Banks Show Different Rates

Regulatory requirements from the Truth in Savings Act (Regulation DD) dictate disclosure rules:

Savings accounts MUST show APY: Protects consumers by showing true earnings
Loans typically show APR: Industry standard for borrowing costs
Credit cards show APR: Not required to disclose APY (which would be higher)
Marketing tactic: Banks highlight whichever number looks better (APY for savings, APR for loans)

How to Use This Calculator

Our APR vs APY calculator helps you:

Convert APR to APY: See true rate with any compounding frequency
Compare multiple accounts: Standardize rates to APY for accurate comparison
Calculate real earnings: See exact dollar impact on any balance
Evaluate compounding effect: Test how daily vs monthly vs quarterly affects returns
Understand loan costs: Calculate true cost of credit card debt with daily compounding
Make informed decisions: Choose best savings account or lowest-cost loan based on facts

For related calculations, explore our Compound Interest Calculator for growth projections, Savings Calculator for goal planning, Loan Calculator for borrowing costs, and Investment Calculator for portfolio returns.

Calculation Type

Input Details

APR vs APY: Understanding the Difference

What is APR (Annual Percentage Rate)?

What is APY (Annual Percentage Yield)?

The Power of Compound Interest

Real-World Applications

For Savers: Maximizing Returns

For Borrowers: Understanding True Cost

When APY Matters Most

Why Banks Show Different Rates

How to Use This Calculator

Related Calculators

Compound Interest

Savings Calculator

Loan Calculator

Investment Calculator

Interest Calculator

Credit Card Payoff

CD Calculator

Retirement Calculator

APR vs APY Calculator - Compound Interest Comparison

Calculation Type

Input Details

APR vs APY: Understanding the Difference

What is APR (Annual Percentage Rate)?

What is APY (Annual Percentage Yield)?

The Power of Compound Interest

Real-World Applications

For Savers: Maximizing Returns

For Borrowers: Understanding True Cost

When APY Matters Most

Why Banks Show Different Rates

How to Use This Calculator

Related Calculators

Compound Interest

Savings Calculator

Loan Calculator

Investment Calculator

Interest Calculator

Credit Card Payoff

CD Calculator

Retirement Calculator