Calculate the Effective Annual Rate (EAR/APY) from nominal interest rates. See the true annual return with different compounding frequencies.
Effective Annual Rate (EAR)
5.1162%
monthly compounding
Nominal Rate (APR)
5.00%
Stated annual rate
Enter nominal rate and compounding frequency
See the difference between nominal and effective rates
Nominal Rate (APR)
5.00%
Stated rate
Effective Rate (EAR/APY)
5.12%
True annual rate
Compounding Effect: With monthly compounding, your 5% nominal rate becomes an effective rate of 5.1162%, adding +0.1162% to your actual annual return.
Mathematical formulas and explanation
Standard Compounding Formula:
EAR = (1 + r/n)^n - 1
Where:
EAR = (1 + 0.0500/12)^12 - 1 = 5.116190%
Why it matters: The effective rate tells you what you actually earn or pay per year when interest compounds. A 5% nominal rate becomes 5.116% with monthly compounding and 5.127% with daily compounding - that's $127 more per $10,000 invested annually.
See how your money grows over time
Initial Amount
$10,000
Interest Earned
$6,470
Future Value
$16,470
After 10 years at 5% nominal rate with monthly compounding, your $10,000 grows to $16,470, earning $6,470 in interest.
See how different compounding affects your 5% nominal rate
| Compounding | Effective Rate | Future Value | Interest |
|---|---|---|---|
| annually | 5.0000% | $16,289 | $6,289 |
| semi annually | 5.0625% | $16,386 | $6,386 |
| quarterly | 5.0945% | $16,436 | $6,436 |
| monthly | 5.1162% | $16,470 | $6,470 |
| weekly | 5.1246% | $16,483 | $6,483 |
| daily | 5.1267% | $16,487 | $6,487 |
| continuous | 5.1271% | $16,487 | $6,487 |
* All calculations based on 5% nominal rate, $10,000 principal, 10 years
Common rates and their effective equivalents
| Account Type | Nominal APR | Compounding | Effective APY |
|---|---|---|---|
| High-Yield Savings | 5.00% | daily | 5.127% |
| CD (Certificate) | 5.50% | monthly | 5.641% |
| Money Market | 4.50% | daily | 4.602% |
| Credit Card | 18.00% | daily | 19.716% |
| Personal Loan | 10.00% | monthly | 10.471% |
| Mortgage | 7.00% | monthly | 7.229% |
* Sample rates for illustration. Actual rates vary by institution and creditworthiness.
The Effective Annual Rate (EAR), also called Annual Percentage Yield (APY), represents the true annual interest rate accounting for compounding. Calculate it using EAR = (1 + r/n)^n - 1, where r is the nominal rate and n is compounding periods per year. For example, a 5% nominal rate compounded monthly yields an EAR of 5.116%, compounded daily yields 5.127%, and continuous compounding yields 5.127%. More frequent compounding always results in higher effective rates.
See how different nominal rates convert with monthly compounding
2 insights based on your inputs
5% is a competitive savings rate in 2025. Your effective rate of 5.12% with monthly compounding is even better.
Switching to daily compounding would give you 0.011% more effective rate - an extra $1 per year.
Explore other tools that might help
The Effective Annual Rate (EAR), also called Annual Percentage Yield (APY), is the actual annual interest rate earned or paid when compounding is taken into account. Unlike the nominal rate (APR), EAR reflects the true return. For example, a 6% nominal rate compounded monthly has an EAR of 6.168%. The formula is EAR = (1 + r/n)^n - 1, where r is the nominal rate and n is the number of compounding periods per year.
APR (Annual Percentage Rate) is the nominal interest rate without accounting for compounding effects. APY (Annual Percentage Yield) is the effective rate that includes compounding and equals EAR. Banks advertise APY on savings accounts because it's higher (better for customers), and APR on loans because it's lower (looks better). A 5% APR compounded monthly equals 5.116% APY.
More frequent compounding results in higher effective rates. For a 6% nominal rate: annual compounding = 6.000% EAR, quarterly = 6.136%, monthly = 6.168%, daily = 6.183%, continuous = 6.184%. The difference grows with higher rates - at 12%: annual = 12.000%, monthly = 12.683%, daily = 12.747%. This is why credit card companies prefer daily compounding.
Continuous compounding is the theoretical limit where interest compounds infinitely often. The formula is EAR = e^r - 1, where e is Euler's number (≈2.71828). A 5% nominal rate with continuous compounding yields 5.127% effective. In practice, daily compounding (5.127%) is virtually identical to continuous, so few real-world applications use true continuous compounding.
Use the formula EAR = (1 + r/n)^n - 1. First, divide the nominal annual rate by the number of compounding periods per year (n). Add 1, raise to the power of n, then subtract 1. For example, 6% compounded monthly: (1 + 0.06/12)^12 - 1 = 1.005^12 - 1 = 0.06168 = 6.168%. Our calculator does this instantly for all compounding frequencies.
Banks show APY (effective rate) on savings accounts because it's higher than APR (nominal rate) when interest compounds, making their rates look more attractive. On loans, they show APR because it looks lower. This is legal and standard practice. Always compare APY to APY and APR to APR when shopping for financial products.
As of 2025, good savings account APYs are 4.5-5.5% for high-yield savings accounts, 5.0-5.5% for CDs, and 4.0-5.0% for money market accounts. Traditional bank savings accounts offer much less (0.01-0.5%). Rates vary with Federal Reserve policy. Always compare APY (not APR) when shopping for savings accounts, and consider FDIC insurance limits.
Yes, but less so. The difference between nominal and effective rates compounds over time. For a 6-month investment at 5% nominal monthly vs annual, the difference is only about $6 per $10,000. Over 10 years, it's about $175. For short-term (under 1 year), the difference is small but not zero. Always use effective rates for accurate comparisons.
Effective Annual Rate (EAR)
5.1162%
monthly compounding
Nominal Rate (APR)
5.00%
Stated annual rate