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Money & Finance

APR vs APY: What's the Difference?

Learn the difference between APR and APY, how compounding interest affects real rates, and how to convert between borrowing and investment yields.

Understanding the Calculation

Financial institutions often market the rate that looks most attractive for their specific product. When banks promote high-yield savings accounts or certificates of deposit (CDs), they advertise APY because compounding makes the projected return look higher. When lenders advertise credit cards, auto loans, or mortgages, they feature APR because the rate appears lower.

Federal regulations govern how each rate is disclosed. In the United States, the Truth in Lending Act (Regulation Z) requires consumer lenders to disclose the APR, which includes both the nominal interest rate and mandatory finance fees like origination points. For savings accounts, the Truth in Savings Act (Regulation DD) requires banks to publish the APY to help savers compare true annual returns.

Understanding the mathematical relationship between the two rates helps you evaluate borrowing costs and investment returns on an equal footing, preventing misleading comparisons between products with different compounding cycles.

The Formula

APR to APY Conversion Formula
APY = (1 + r / n)^n - 1

Dividing the nominal rate by the number of compounding periods produces the periodic interest rate. Compounding that periodic rate across n intervals accounts for interest earned on earlier interest payments.

Variables & Definitions

APY— Annual Percentage Yield
The effective annual return or borrowing rate after compounding.
r— Stated Annual Interest Rate (APR)
The nominal annual percentage rate expressed as a decimal.
n— Compounding Periods Per Year
How often interest is calculated and added to principal (12 for monthly, 365 for daily).

Worked Example

Worked Example: Converting 6.0% Monthly Compounding APR to APY

An investor deposits $10,000 into a high-yield savings account offering a stated nominal rate of 6.0% APR, with interest compounded at the end of each month.

Starting Inputs
  • Initial Deposit:$10,000
  • Stated Annual Rate (r):6.0% (0.06)
  • Compounding Frequency (n):12 periods per year (monthly)
Step-by-Step Calculation
  1. 1

    Determine the monthly periodic rate

    Divide the nominal annual rate by 12 months: 0.06 / 12 = 0.005 (0.5% per month).

    r / n = 0.06 / 12 = 0.005
  2. 2

    Calculate the annual compounding multiplier

    Add 1 to the periodic rate and raise the sum to the 12th power: (1 + 0.005)^12 = (1.005)^12 ≈ 1.061678.

    (1.005)^12 ≈ 1.061678
  3. 3

    Subtract 1 to isolate the effective rate

    Subtract 1 from the multiplier: 1.061678 - 1 = 0.061678, which equals 6.168% APY.

    Result: APY = 6.168%
  4. 4

    Compare total dollar interest earned after one year

    Without compounding (simple APR), $10,000 * 6.0% yields $600.00. With monthly compounding (APY), the account balance reaches $10,616.78, earning $616.78 in total interest.

    Result: Additional earnings from compounding: $16.78
Conclusion: A 6.0% APR compounded monthly corresponds to an effective annual yield of 6.168% APY. On a $10,000 balance, monthly compounding produces an extra $16.78 in annual return compared to simple interest.

Calculate Your Own Numbers

Put these formulas into practice with our free, in-browser calculators:

Compound Interest Calculator

Model growth across daily, monthly, and annual compounding schedules.

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Savings Calculator

Project how regular deposits and compound yields build your savings goal.

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Loan Calculator

Calculate borrowing costs and installment schedules across loan terms.

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What the Results Mean For You

  • Compounding frequency increases returns, but with diminishing returns: Daily compounding (n = 365) on 6.0% APR yields an APY of 6.183%, earning only $1.53 more per year on a $10,000 balance than monthly compounding.
  • For credit card borrowers, compounding accelerates debt: A credit card advertising a 24.0% APR with daily compounding actually carries an effective annual rate (APY) of 27.11%, meaning unpaid balances compound faster than simple annual interest implies.
  • Always convert to the same metric before choosing: When comparing savings products or loans from different providers, compare APY to APY for deposits, or compare loan APRs that incorporate identical fee structures.

Common Pitfalls & Mistakes

Directly comparing a loan's APR to a savings account's APY

Because mortgage APRs include upfront closing fees and points, they cannot be directly compared against a bank deposit's APY without isolating the underlying interest rate.

Assuming annual percentage rate and annual yield are interchangeable

Using APR in place of APY for long-term compound growth projections understates future balances, while using APY instead of APR for simple loan payments overstates the scheduled installment.

Expecting continuous compounding to produce massive gains

Mathematically, the compounding multiplier approaches e^r as compounding frequency reaches infinity. Beyond monthly compounding, the practical monetary difference for consumer accounts is minimal.

Authoritative References & Sources

All formula representations and regulatory context are verified against authoritative public sources:

  • Truth in Savings Act (Regulation DD) Consumer Compliance GuideFederal Deposit Insurance Corporation (FDIC)

    Federal guidelines governing annual percentage yield calculation and disclosure rules.

    Visit source documentation
  • Truth in Lending (Regulation Z) Annual Percentage Rate RulesConsumer Financial Protection Bureau (CFPB)

    Statutory standards for APR calculation and finance charge disclosure.

    Visit source documentation