Effective Interest Rate Calculator

Calculate the Effective Annual Rate (EAR/APY) from nominal interest rates. See the true annual return with different compounding frequencies.

Effective Rate Results

Effective Annual Rate (EAR)

5.1162%

monthly compounding

Nominal Rate (APR)

5.00%

Stated annual rate

Rate Difference+0.1162%
Future Value$16,470
Interest Earned$6,470

Interest Rate Details

Enter nominal rate and compounding frequency

%

EAR vs APR Comparison

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.

How EAR is Calculated

Mathematical formulas and explanation

Standard Compounding Formula:

EAR = (1 + r/n)^n - 1

Where:

  • • r = nominal annual rate (5% = 0.0500)
  • • n = compounding periods per year (12)

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.

Investment Growth Example

See how your money grows over time

$
years

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.

Compare All Compounding Frequencies

See how different compounding affects your 5% nominal rate

CompoundingEffective RateFuture ValueInterest
annually5.0000%$16,289$6,289
semi annually5.0625%$16,386$6,386
quarterly5.0945%$16,436$6,436
monthly5.1162%$16,470$6,470
weekly5.1246%$16,483$6,483
daily5.1267%$16,487$6,487
continuous5.1271%$16,487$6,487

* All calculations based on 5% nominal rate, $10,000 principal, 10 years

Real-World Examples

Common rates and their effective equivalents

Account TypeNominal APRCompoundingEffective APY
High-Yield Savings5.00%daily5.127%
CD (Certificate)5.50%monthly5.641%
Money Market4.50%daily4.602%
Credit Card18.00%daily19.716%
Personal Loan10.00%monthly10.471%
Mortgage7.00%monthly7.229%

* Sample rates for illustration. Actual rates vary by institution and creditworthiness.

Quick Answer: What is Effective Interest Rate?

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.

Key Facts About Effective Interest Rates

  • EAR (Effective Annual Rate) and APY (Annual Percentage Yield) are the same thing - the true annual return
  • Formula: EAR = (1 + r/n)^n - 1, where r is nominal rate and n is compounding periods per year
  • More frequent compounding increases the effective rate: annual < semi-annual < quarterly < monthly < daily < continuous
  • A 5% nominal rate becomes 5.116% with monthly compounding and 5.127% with daily compounding
  • APR (Annual Percentage Rate) is the nominal rate; APY/EAR is the effective rate after compounding
  • Continuous compounding uses e^r - 1 and represents the theoretical maximum effective rate
  • Banks advertise APY on savings accounts (higher number) and APR on loans (lower number)
  • The difference between nominal and effective rates increases with higher rates and more frequent compounding

What if the nominal rate changed?

See how different nominal rates convert with monthly compounding

0.5%5%20%

Personalized Insights

2 insights based on your inputs

Good Savings Rate

5% is a competitive savings rate in 2025. Your effective rate of 5.12% with monthly compounding is even better.

Consider Daily Compounding

Switching to daily compounding would give you 0.011% more effective rate - an extra $1 per year.

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Frequently Asked Questions

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.