APY to APR Calculator | Convert Yield to Rate

  • Adam
  • November 13, 2025

Free APY to APR calculator. Convert Annual Percentage Yield to Rate (and vice versa) with daily, monthly, quarterly compounding. Compare savings & loan rates.

APY to APR Calculator – Convert Annual Percentage Yield & Rate

The APY to APR calculator converts between Annual Percentage Yield (APY) and Annual Percentage Rate (APR) based on compounding frequency. APY shows the actual annual return including compound interest effects, while APR represents the simple annual rate without compounding. Use this bidirectional calculator to compare savings accounts (typically quoted in APY) with loans or credit cards (quoted in APR), or to understand how compounding frequency—daily, monthly, quarterly, or annually—affects your true earnings or borrowing costs.

📈 APR to APY Converter

Convert Annual Percentage Rate to Yield

Enter APR as percentage (e.g., 5.00)
How often interest compounds
Initial investment/deposit (optional)

APY Conversion Results

APR (Input)
5.00%
APY (Output)
5.12%
Compounding
Monthly

Interest Comparison on $10,000

Metric Value
APR (Simple) 5.00%
APY (Compound) 5.12%
Compounding Periods/Year 12
Interest with APR (simple) $500
Interest with APY (compound) $512
Extra Earnings from Compounding $12

📉 APY to APR Converter

Convert Annual Percentage Yield to Rate

Enter APY as percentage (e.g., 5.12)
How often interest compounds
Initial investment/deposit (optional)

APR Conversion Results

APY (Input)
5.12%
APR (Output)
5.00%
Compounding
Monthly

Interest Breakdown on $10,000

Metric Value
APY (Compound) 5.12%
APR (Simple) 5.00%
Compounding Periods/Year 12
Actual Annual Earnings (APY) $512
Nominal Rate Needed (APR) 5.00%

Understanding APR vs APY

Annual Percentage Rate (APR) and Annual Percentage Yield (APY) are two different ways of expressing interest rates, and understanding the distinction is crucial for making informed financial decisions about savings, investments, and loans.

What is APR (Annual Percentage Rate)?

APR is the simple annual interest rate without accounting for compounding within the year. It's the nominal rate that's applied to your principal. APR is commonly used for:

  • Credit cards: Shows the yearly cost of borrowing
  • Personal loans: Indicates the annual interest charge
  • Mortgages: Displays the base interest rate
  • Auto loans: Shows simple annual rate

What is APY (Annual Percentage Yield)?

APY accounts for compound interest—the interest earned on both your principal and previously earned interest. APY always equals or exceeds APR because it includes compounding effects. APY is commonly used for:

  • Savings accounts: Shows actual annual return
  • CDs (Certificates of Deposit): Displays true yield
  • Money market accounts: Indicates real earnings
  • High-yield savings: Shows compound growth

Key Difference: APR tells you the rate, APY tells you the yield. For savings, higher APY is better (you earn more). For loans, lower APR is better (you pay less). The more frequently interest compounds, the bigger the gap between APR and APY.

APR to APY Conversion Formula

Converting APR to APY requires accounting for the compounding frequency:

APR to APY Formula:

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

Where:

  • APY = Annual Percentage Yield (as decimal)
  • APR = Annual Percentage Rate (as decimal)
  • n = Number of compounding periods per year

Example APR to APY Conversion:

Given: 5% APR with monthly compounding (n = 12)

Step 1: Convert APR to decimal = 5% = 0.05

Step 2: Divide by compounding periods = 0.05 / 12 = 0.004167

Step 3: Add 1 = 1 + 0.004167 = 1.004167

Step 4: Raise to power of n = (1.004167)^12 = 1.05116

Step 5: Subtract 1 = 1.05116 - 1 = 0.05116

Result: APY = 5.12% (compared to 5% APR)

Impact: On $10,000, you earn $512 instead of $500—an extra $12 from compounding

APY to APR Conversion Formula

Converting APY back to APR (nominal rate) requires the inverse calculation:

APY to APR Formula:

APR = n × [(1 + APY)^(1/n) - 1]

Where:

  • APR = Annual Percentage Rate (as decimal)
  • APY = Annual Percentage Yield (as decimal)
  • n = Number of compounding periods per year

Example APY to APR Conversion:

Given: 5.12% APY with monthly compounding (n = 12)

Step 1: Convert APY to decimal = 5.12% = 0.0512

Step 2: Add 1 = 1 + 0.0512 = 1.0512

Step 3: Take nth root = (1.0512)^(1/12) = 1.004167

Step 4: Subtract 1 = 1.004167 - 1 = 0.004167

Step 5: Multiply by n = 0.004167 × 12 = 0.05

Result: APR = 5.00% (the nominal rate needed to achieve 5.12% APY)

Impact of Compounding Frequency

Compounding frequency dramatically affects the difference between APR and APY:

Compounding Periods/Year (n) 5% APR → APY 10% APR → APY Difference
Annually 1 5.00% 10.00% 0.00%
Semi-Annually 2 5.06% 10.25% +0.06% / +0.25%
Quarterly 4 5.09% 10.38% +0.09% / +0.38%
Monthly 12 5.12% 10.47% +0.12% / +0.47%
Daily 365 5.13% 10.52% +0.13% / +0.52%

Key Insight: The higher the APR, the more significant the compounding effect. At 10% APR with daily compounding, you earn 10.52% APY—an extra 0.52% annually. On $100,000, that's an additional $520 per year just from more frequent compounding. Always compare APY to APY and APR to APR—never mix them.

Real-World APY and APR Examples

Savings Account Comparison

Two banks advertise "5%" rates but use different compounding:

  • Bank A: 5% APR, annual compounding = 5.00% APY → Earns $500 on $10,000
  • Bank B: 5% APR, daily compounding = 5.13% APY → Earns $513 on $10,000
  • Result: Bank B pays $13 more per year despite same stated "5%" rate

Credit Card APR

Credit card with 18% APR, compounded daily:

  • Stated APR: 18.00%
  • Actual APY: 19.72% (due to daily compounding)
  • On $10,000 balance: You pay $1,972 in interest, not $1,800
  • Impact: $172 more in interest than simple calculation suggests

When to Use APR vs APY

Use APR When:

  • Comparing loans: Credit cards, mortgages, auto loans typically quoted in APR
  • Simple interest: Some loans compound annually or use simple interest
  • Regulatory requirements: Truth in Lending Act requires APR disclosure
  • Nominal rate needed: You want the base rate without compounding

Use APY When:

  • Comparing savings: High-yield savings, CDs, money market accounts
  • True earnings: You want to know actual annual return
  • Investment accounts: Shows compound growth effect
  • Frequent compounding: Daily or monthly compounding makes APY more accurate

⚠️ Common Mistake: Never compare APR from one account to APY from another—you're comparing apples to oranges. A savings account advertising "5% APY" is better than one advertising "5% APR" even though the numbers look the same. Always convert to the same metric (preferably APY for savings, APR for loans) before comparing.

Frequently Asked Questions

What is the difference between APR and APY?
APR (Annual Percentage Rate) is the simple annual interest rate without compounding effects. APY (Annual Percentage Yield) includes compound interest, showing the actual annual return. Formula: APY = (1 + APR/n)^n - 1, where n = compounding periods. Example: 5% APR with monthly compounding = 5.12% APY. APY is always equal to or higher than APR. For savings, compare APY (shows true earnings). For loans, compare APR (shows base rate). The more frequent the compounding (daily vs annually), the bigger the gap between APR and APY.
How do you convert APR to APY?
Use formula: APY = (1 + APR/n)^n - 1. Where APR is decimal (5% = 0.05), n = compounding periods/year. Example: 6% APR, monthly compounding: (1 + 0.06/12)^12 - 1 = (1.005)^12 - 1 = 1.06168 - 1 = 0.06168 = 6.17% APY. Steps: 1) Convert APR to decimal, 2) Divide by n, 3) Add 1, 4) Raise to power n, 5) Subtract 1, 6) Convert to percentage. Daily compounding (n=365) gives higher APY than monthly (n=12) or annual (n=1).
How do you convert APY to APR?
Use formula: APR = n × [(1 + APY)^(1/n) - 1]. Where APY is decimal, n = compounding periods/year. Example: 6.17% APY, monthly compounding: 12 × [(1.0617)^(1/12) - 1] = 12 × [1.005 - 1] = 12 × 0.005 = 0.06 = 6% APR. This finds the nominal rate needed to achieve the given APY. Steps: 1) Convert APY to decimal, 2) Add 1, 3) Take nth root, 4) Subtract 1, 5) Multiply by n, 6) Convert to percentage. Used to compare advertised APY to underlying APR.
Is higher APY or APR better for savings?
Higher APY is better for savings—shows actual annual earnings including compound interest. Always compare APY to APY for savings accounts. Example: Account A: 5% APR (annual compounding) = 5.00% APY. Account B: 4.88% APR (daily compounding) = 5.00% APY—both earn same amount. Account C: 5% APY means you definitely earn 5% regardless of compounding. For loans, lower APR is better (less interest paid). APY measures what you earn (savings), APR measures what you're charged (loans). Don't compare APR to APY—convert both to same metric first.
Why is APY higher than APR?
APY is higher than APR because APY includes compound interest effects—earning interest on interest. The more frequently interest compounds, the higher APY vs APR. Examples: 5% APR compounded annually = 5.00% APY (no difference). 5% APR compounded monthly = 5.12% APY (0.12% higher). 5% APR compounded daily = 5.13% APY (0.13% higher). Formula: APY = (1 + APR/n)^n - 1. Each compounding period adds interest to principal, which then earns more interest. Higher rates show bigger gap: 10% APR daily = 10.52% APY (0.52% difference). APY can never be lower than APR.
What compounding frequency is best?
For savings: Daily compounding is best—maximizes APY and earnings. Example: $10,000 at 5% APR: Annual compounding = $500 interest (5.00% APY). Monthly compounding = $512 interest (5.12% APY). Daily compounding = $513 interest (5.13% APY). Daily earns $13 more than annual. For loans: Annual compounding is best—minimizes APY and cost. On $10,000 at 18% APR: Annual = $1,800 interest (18.00% APY). Daily = $1,972 interest (19.72% APY). Annual saves $172. Continuous compounding gives theoretical maximum APY: e^r - 1 (where e ≈ 2.718).
Can APR and APY be the same?
Yes, APR equals APY only with annual compounding (n=1) or no compounding. Formula: APY = (1 + APR/1)^1 - 1 = APR. Example: 5% APR compounded once yearly = 5% APY exactly. Any more frequent compounding (monthly, daily) makes APY higher than APR. Some simple interest loans have no compounding, so APR = APY. Most savings accounts compound more than annually, making APY > APR. If you see APR and APY listed as same percentage, compounding is annual. This is rare for modern savings accounts (usually daily/monthly compounding).

Practical Tips for Using APR and APY

For Savers and Investors

  • Always compare APY: Ignore stated APR, only compare APY between savings accounts
  • Seek daily compounding: Maximizes earnings, especially on high-yield savings
  • Calculate true return: Use APY calculator to find real annual earnings
  • Watch for tricks: Some banks advertise APR to look better—convert to APY
  • Compound frequency matters: 5% APR daily beats 5.1% APR annually

For Borrowers

  • Compare APR on loans: Lower APR = less interest paid (if same compounding)
  • Check compounding: Daily compounding on credit cards makes APR worse
  • Calculate APY on debt: See true annual cost including compound effect
  • Pay more frequently: Biweekly payments reduce compound interest impact
  • Understand credit cards: 18% APR ≈ 19.7% APY with daily compounding

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