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Effective Annual Yield Calculator
Convert nominal interest rates to effective annual yield (EAY/APY). Compare compounding frequencies and see the difference in future value.
Second rate for side-by-side comparison
Effective Annual Yield⧉
5.1162%
Nominal 5% compounded 12× per year
Comparison EAY⧉
5.6145%
Nominal 5.5% compounded 4× per year
Continuous EAY⧉
5.1271%
Maximum possible with continuous compounding
Future Value⧉
$12,833.59
After 5 years with compound interest
Total Interest Earned⧉
$2,833.59
Compound interest earned over the period
Compounding Benefit⧉
$333.59
Extra earned vs simple interest
Rate Comparison
Option A (5%, 12×)
5.116%
Option B (5.5%, 4×)
5.614%
Winner: Option B (0.4983% difference)
Compounding Frequency Impact
| Frequency | Periods/Year | EAY | Future Value (5yr) |
|---|---|---|---|
| Annual | 1 | 5.0000% | $12,762.82 |
| Semi-Annual | 2 | 5.0625% | $12,800.85 |
| Quarterly | 4 | 5.0945% | $12,820.37 |
| Monthly | 12 | 5.1162% | $12,833.59 |
| Weekly | 52 | 5.1246% | $12,838.71 |
| Daily | 365 | 5.1267% | $12,840.03 |
| Continuous | ∞ | 5.1271% | $12,840.25 |
Planning notes, formulas, and examples
About the Effective Annual Yield Calculator
When comparing savings accounts, CDs, or loans, the nominal (stated) interest rate can be misleading. A 5% rate compounded monthly actually yields more than a 5% rate compounded annually. The Effective Annual Yield (EAY), also known as APY, accounts for this compounding effect and gives you the true annual return.
The difference between nominal and effective rates may seem small for low rates and common compounding, but it becomes significant for higher rates, more frequent compounding, and longer time horizons. A credit card charging 24% APR compounded daily has an effective rate of 27.11% — a meaningful difference.
This calculator converts any nominal rate to its effective annual yield based on compounding frequency, and lets you compare two different rate/frequency combinations side by side. The frequency impact table shows how the same nominal rate produces different effective yields across compounding intervals, from annual to continuous, which is the useful comparison when products advertise rates in different ways.
When This Page Helps
Use this calculator when you need to compare savings, CDs, loans, or APR/APY offers on the same basis. It is especially useful when one product emphasizes the nominal rate and another emphasizes the yield, because compounding frequency can change the real result more than the headline rate suggests.
How to Use the Inputs
- Enter the nominal (stated) annual interest rate.
- Select the compounding frequency (monthly, daily, etc.).
- Enter an investment amount and time horizon for future value projection.
- Enter a second rate and frequency for side-by-side comparison.
- Review the EAY, future value, and compounding frequency impact table.
- Use the comparison feature to decide between two competing offers.
Formula used
EAY = (1 + r/n)^n − 1
Continuous EAY = e^r − 1
Future Value = Principal × (1 + EAY)^Years
Where r = nominal annual rate, n = compounding periods per year.Example Calculation
Result: EAY = 5.1162%
A 5% nominal rate compounded monthly yields an effective annual rate of 5.1162%. On $10,000 over 5 years, this compounds to $12,834 vs $12,763 with annual compounding — a $71 benefit from monthly compounding.
Tips & Best Practices
- When comparing bank accounts, always compare APY (effective rate), not the nominal rate.
- For savings, seek higher compounding frequency. For loans, lower frequency saves money.
- The difference between daily and continuous compounding is negligible in practice.
- Credit card APR of 24% compounded daily is really 27.11% effective — always check.
- Use this calculator to compare a CD offer against a high-yield savings account fairly.
Why Effective Yield Matters
Nominal rates tell you the stated annual percentage, but they do not tell you how often interest is added back to the balance. APY or effective annual yield does. That is why a savings account with a 5.00% nominal rate compounded monthly produces a higher one-year return than the same nominal rate compounded annually.
Comparing Compounding Frequencies
The gap between nominal and effective rates grows when compounding becomes more frequent. Annual compounding gives one interest credit per year, monthly gives twelve, daily gives 365, and continuous compounding is the mathematical upper limit. In practice, monthly versus daily matters more than daily versus continuous for most consumer products, but the difference is still worth measuring when rates are high.
Savings vs Borrowing
For savers, a higher effective yield is better because the balance grows faster. For borrowers, the same math works against you: more frequent compounding increases the real borrowing cost. Using EAY lets you compare bank deposits, CDs, credit products, and investment projections without switching between inconsistent marketing terms.
Sources & Methodology
Last updated:
Methodology
This calculator converts a nominal annual rate into an effective annual yield by applying the selected compounding frequency across a full year. It also projects a future value from the resulting effective rate so users can see the practical dollar impact of comparing annual, monthly, daily, or continuous compounding on the same principal.
The APY comparison is a rate-normalization worksheet. It does not account for account fees, promotional tiers, or special disclosure rules beyond the compounding math itself, so actual bank-product comparisons still depend on the terms of the specific account.
Sources
- Effective Annual Rate (Investor.gov / U.S. Securities and Exchange Commission)
- Appendix A to Part 1030 — Annual Percentage Yield Calculation (Consumer Financial Protection Bureau)
Frequently Asked Questions
APR is the nominal annual rate without compounding. APY (= EAY) includes the effect of compounding. APY is always equal to or higher than APR.
Yes, but the difference decreases as frequency increases. Monthly to daily is a bigger jump than daily to continuous for most real-world rates.
It is the mathematical limit of compounding infinitely often. The formula uses e^r. It produces the maximum possible effective rate for a given nominal rate.
Always compare effective rates (APY) between products. A 4.9% APY is better than a 5.0% APR compounded annually (which is exactly 5.0% APY), but worse than 5.0% compounded monthly (5.12% APY).
For borrowers, more frequent compounding means you pay more interest. Credit cards compounding daily cost more than the stated APR suggests.
For fixed-rate products (CDs, fixed savings), yes. For variable-rate products, the APY changes when the underlying rate changes.
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