APR vs APY Calculator
Understand the difference between APR and APY. Compare simple interest vs compound interest rates and see how compounding frequency affects your money.
Rate Details
APR = Simple interest without compounding
Rate Comparison
APR (Simple Interest)
0.000%
No compounding effect
APY (Compound Interest)
0.000%
With monthly compounding
Rate Difference
0.000%
0.00% higher APY
Dollar Value Comparison
Simple Interest (APR)
Compound Interest (APY)
Over 1 year
Simple Interest vs Compound Interest Growth
Compounding Frequency Comparison
See how the same APR (5.000%) converts to different APY values based on compounding frequency:
| Frequency | Times/Year | APR | APY | Difference |
|---|---|---|---|---|
| daily | 365 | 5.000% | 5.127% | +0.127% |
| monthly(Selected) | 12 | 5.000% | 5.116% | +0.116% |
| quarterly | 4 | 5.000% | 5.095% | +0.095% |
| annually | 1 | 5.000% | 5.000% | +0.000% |
More frequent compounding results in a higher effective annual yield (APY), even when the APR stays the same.
Understanding APR vs APY: The Complete Guide
APR (Annual Percentage Rate) and APY (Annual Percentage Yield) are two of the most important concepts in personal finance, yet they're often misunderstood or used interchangeably. While both represent annual interest rates, they differ fundamentally in how they account for the effects of compounding. Understanding this difference can help you make better financial decisions, whether you're comparing savings accounts, evaluating loan offers, or analyzing investment returns.
The key distinction is simple: APR represents simple interest without accounting for compounding, while APY includes the effects of compound interest. This difference might seem minor at first glance, but it can result in substantially different returns or costs over time. Banks and financial institutions strategically use these terms - they advertise APR for loans (making rates appear lower) and APY for savings accounts (making returns appear higher). By understanding both, you can see through marketing tactics and make truly informed comparisons.
What is APR?
APR, or Annual Percentage Rate, is the annualized representation of the interest rate charged on borrowed money or earned on invested money, calculated using simple interest. It does not account for the effects of compounding during the year. When you see an APR of 5%, it means you'll pay or earn exactly 5% of the principal amount over one year, with no additional interest being calculated on previously accrued interest.
For example, if you borrow $10,000 at 5% APR for one year, you would owe $500 in interest, bringing your total amount due to $10,500. The calculation is straightforward: Principal × Rate × Time = $10,000 × 0.05 × 1 = $500.
APR is commonly used for credit cards, personal loans, auto loans, and mortgages. Federal law requires lenders to disclose the APR on most loan products, making it a standardized metric for comparison shopping.
What is APY?
APY, or Annual Percentage Yield, is the real rate of return on an investment or the real cost of a loan when accounting for the effects of compounding interest. Unlike APR, APY includes the impact of interest being calculated on previously earned or charged interest. This makes APY a more accurate representation of what you'll actually earn or pay over the course of a year.
Using the same $10,000 example with 5% APR compounded monthly, after one year you would have $10,511.62, not just $10,500. That extra $11.62 comes from interest compounding on itself throughout the year. While this might seem insignificant, over longer time periods and with larger amounts, the compounding effect becomes substantial.
The Mathematics Behind APR and APY
Converting APR to APY
The formula for calculating APY from APR is:
APY = (1 + APR/n)^n - 1
- •n = Number of compounding periods per year
- •Daily compounding: n = 365
- •Monthly compounding: n = 12
- •Quarterly compounding: n = 4
- •Annual compounding: n = 1
For example, converting 6% APR with monthly compounding: APY = (1 + 0.06/12)^12 - 1 = 6.168%. The 0.168% difference represents the additional return from compound interest.
How Compounding Frequency Affects Your Money
5% APR on $10,000 Over One Year
- •Annual (n=1): APY = 5.000% | Balance = $10,500.00
- •Quarterly (n=4): APY = 5.095% | Balance = $10,509.45
- •Monthly (n=12): APY = 5.116% | Balance = $10,511.62
- •Daily (n=365): APY = 5.127% | Balance = $10,512.67
Moving from annual to daily compounding adds an extra $12.67 in earnings on a $10,000 balance. While this might seem modest, the effect magnifies significantly with higher rates, larger balances, and longer time periods. On a $100,000 balance over 10 years at 5%, daily compounding would earn you approximately $1,270 more than annual compounding.
Why Banks Use APR for Loans and APY for Savings
For Loans (Credit Cards, Mortgages, Auto Loans)
Banks advertise the APR because it's the lower number. If a credit card has an APR of 18% with daily compounding, the actual APY you're paying is approximately 19.72%. That's nearly 2 percentage points higher! On a $5,000 balance, that's the difference between $900 and $986 in annual interest.
For Savings Accounts and CDs
Conversely, banks advertise APY for deposit accounts because it's the higher number and makes their products look more attractive. If a savings account offers "4.5% APY," the actual APR is approximately 4.404%.
Know What You're Comparing
This isn't necessarily deceptive - banks are following regulations. The Truth in Savings Act mandates APY disclosure for deposits, while the Truth in Lending Act requires APR disclosure for loans. Understanding why each term is used helps you make accurate comparisons.
Real-World Applications and Examples
Practical Scenarios
- •Comparing Savings Accounts: Bank A offers "3.0% APY" vs Bank B's "2.95% APR compounded daily" (APY = 2.99%). Bank A is only marginally better - consider fees and features too.
- •Credit Card Balance Transfer: Moving from 18% APR daily (APY = 19.72%) to 15% APR monthly (APY = 16.08%) saves $364/year on a $10,000 balance.
- •Long-Term Investing: $25,000 at 7% over 30 years: Simple interest = $77,500 total vs Daily compounding = $195,517 total. The difference is $118,017!
How to Make Better Financial Decisions
Smart Money Strategies
- 1.Convert to Same Basis: Always compare APR to APR or APY to APY, preferably APY for accuracy.
- 2.Consider Compounding Frequency: More frequent = better for savings, worse for debt.
- 3.Use APY for Long-Term Planning: APR underestimates both returns and costs over time.
- 4.Factor in All Fees: APY doesn't include maintenance fees - calculate net APY for true comparison.
- 5.Prioritize High-APR Debt: The compounding effect works most powerfully against you on high-interest debt.
- 6.Maximize Compounding on Investments: A 7% vs 6% APY on $10,000 over 40 years = $47,000 difference!
Additional Frequently Asked Questions
What's the main difference between APR and APY?
APR is the simple interest rate without accounting for compounding, while APY includes the effects of compound interest. APY is always equal to or higher than APR for the same interest rate, with the difference depending on compounding frequency.
Can APY ever be lower than APR?
No, APY cannot be lower than APR for positive interest rates. At minimum, with annual compounding (n=1), APY equals APR. With any more frequent compounding, APY will always be higher due to the compound interest effect.
Do banks have to disclose both APR and APY?
Banks are required to disclose the appropriate rate based on the product type. The Truth in Savings Act requires APY disclosure for deposit accounts (savings, CDs), while the Truth in Lending Act requires APR disclosure for most loan products. Both rates should be available in account agreements and disclosures.
How much difference does compounding frequency really make?
The impact varies with the interest rate and time period. For a 5% rate over one year, moving from annual to daily compounding adds approximately 0.127 percentage points. This might seem small, but on $100,000 over 30 years, the difference between annual and daily compounding is approximately $11,850 in additional earnings.
Should I always choose daily compounding over monthly?
While daily compounding is mathematically superior to monthly compounding at the same APR, the difference is often minimal. Consider the entire package: fees, minimum balances, accessibility, and other features. Sometimes an account with monthly compounding but no fees and better terms is superior to one with daily compounding but high fees.
What's the highest possible APY for a given APR?
The theoretical maximum is continuous compounding, calculated as e^APR - 1, where e is Euler's number (2.71828). For 5% APR, continuous compounding yields approximately 5.1271% APY. Daily compounding (5.1268% APY) is already extremely close to this theoretical maximum.
Does mortgage APR include closing costs and fees?
Yes, mortgage APR is required to include most loan fees and closing costs spread over the loan term, making it higher than the note rate. This makes mortgage APR different from the simple APR definition and more useful for comparing total loan costs. However, it still doesn't fully account for compounding effects.
Is APY the same as compound annual growth rate (CAGR)?
They're similar but not identical. APY assumes consistent interest rate and regular compounding throughout the year. CAGR is typically used for investments that don't have regular compounding but instead represent the annualized return between a starting and ending value. CAGR smooths out volatility over multiple years to show average annual return.
Why do banks advertise APR for loans and APY for savings?
Banks strategically choose which rate to advertise to make their products appear more attractive. APR is the lower number (making loans look cheaper), while APY is the higher number (making savings look more lucrative). This is legal marketing psychology - they must still disclose both rates in account agreements.
How do I convert APR to APY manually?
Use the formula: APY = (1 + APR/n)^n - 1, where n is the number of compounding periods per year. For example, with 5% APR and monthly compounding (n=12): APY = (1 + 0.05/12)^12 - 1 = 5.116%. This calculator performs this conversion automatically for you.