Effective Annual Rate and Compounding Frequency

Updated for the 2026-2027 CFA® Level I curriculum.

A quoted annual rate and an effective annual rate can differ when interest compounds more than once a year. The effective annual rate, or EAR, captures the full one-year effect of that compounding.

For CFA Level I, you should be able to move between the stated annual rate, periodic rate, and EAR. You should also know how compounding frequency affects the final result.

Key Takeaways

• The stated annual rate is the quoted rate before intra-year compounding.

• The periodic rate equals the stated annual rate divided by the number of compounding periods.

• EAR measures the full compound return over one year.

• EAR equals the stated annual rate when compounding occurs once per year.

• More frequent compounding raises EAR when the stated annual rate remains unchanged.

• Rates with different compounding frequencies should be converted to EAR before comparison.

What You Need to Know for CFA Level I

EAR questions mainly test whether you keep the rate and compounding period aligned.

Focus on the following:

• Identify the number of compounding periods represented by inline equation code .

• Convert the stated annual rate to decimal form.

• Divide the stated annual rate by inline equation code to find the periodic rate.

• Use the same value of inline equation code as the exponent.

• Subtract 1 after compounding.

• Interpret EAR as the compound rate earned or charged over one full year.

• Compare rates only after converting them to the same annual basis.

What Is the Effective Annual Rate?

The effective annual rate measures the actual compound growth produced over one year. It incorporates the interest earned on earlier interest payments during the year.

This makes EAR useful when two rates use different compounding conventions. A rate compounded quarterly and a rate compounded monthly cannot be compared fairly from their quoted annual rates alone. Converting both to EAR places them on the same one-year basis.

For an investment, a higher EAR represents a higher effective annual return, all else equal. For borrowing, a higher EAR represents a higher annual interest cost before any additional fees or charges.

EAR focuses on the rate calculation. Risk, liquidity, taxes, fees, and other investment features still need separate consideration.

Stated Annual Rate, Periodic Rate, and EAR

These three measures describe different parts of the same calculation.

Using symbols:

• Inline equation code = stated annual rate

• Inline equation code = number of compounding periods per year

• Inline equation code = periodic interest rate

The periodic rate and the number of periods must represent the same frequency. With monthly compounding, divide the stated annual rate by 12 and use 12 as the exponent.

Common Compounding Frequencies

Daily-compounding questions may use 365 days or another stated convention. Follow the information provided rather than assuming a day count.

Effective Annual Rate Formula

Where:

• Inline equation code = effective annual rate

• Inline equation code = stated annual rate

• Inline equation code = number of compounding periods per year

• Inline equation code = periodic interest rate

[INSERT effective-annual-rate-formula-card.png HERE]

You can work through the formula in four steps:

1. Convert the stated annual rate to decimal form.

2. Divide it by the number of compounding periods.

3. Add 1 and raise the result to the power of inline equation code m.

4. Subtract 1 and convert the result back to a percentage.

For example, a stated annual rate of 8% compounded quarterly has a periodic rate of:

The 2% periodic rate is then compounded four times during the year.

How Does Compounding Frequency Affect EAR?

More frequent compounding gives interest more opportunities to earn additional interest during the year.

Consider a stated annual rate of 9.00%. The stated rate stays fixed while the compounding frequency changes.

Under annual compounding, the full 9% is credited once at the end of the year. Under monthly compounding, interest is credited 12 times, allowing each earlier interest payment to begin earning interest sooner.

The increase becomes smaller as compounding grows more frequent. Moving from annual to semiannual compounding has a larger effect than moving from quarterly to monthly compounding.

Continuous compounding represents the limiting case as the number of compounding periods grows indefinitely. It is covered separately in the study note on continuously compounded returns.

When Does EAR Equal the Stated Annual Rate?

EAR equals the stated annual rate when interest compounds once per year.

With annual compounding, inline equation code . Substituting this into the formula gives:

For example, a stated annual rate of 7% compounded annually has an EAR of 7%.

When compounding occurs more than once per year and the stated rate is positive, EAR exceeds the stated annual rate.

How to Compare Rates With Different Compounding Frequencies

Convert each quoted rate to EAR before deciding which one offers the higher effective annual return.

Use this process:

1. Identify the stated annual rate for each option.

2. Identify the compounding frequency for each option.

3. Calculate the periodic rate.

4. Calculate the EAR.

5. Compare the resulting effective annual rates.

The stated rate and compounding frequency work together. A lower quoted rate can sometimes produce a competitive EAR through more frequent compounding, while a sufficiently higher quoted rate may still produce the greater EAR with less frequent compounding.

Worked Example

Two deposits quote different stated annual rates and use different compounding frequencies:

• Investment A: 9.60% stated annual rate, compounded quarterly

• Investment B: 9.50% stated annual rate, compounded monthly

Which investment provides the higher effective annual return?

Step 1: Calculate the EAR for Investment A

Investment A compounds quarterly, so inline equation code .

Its periodic rate is:

Apply the EAR formula:

Step 2: Calculate the EAR for Investment B

Investment B compounds monthly, so inline equation code .

Its periodic rate is:

Apply the EAR formula:

Step 3: Compare the Results

Investment A provides the slightly higher effective annual return.

Investment B compounds more often, but Investment A begins with the higher stated annual rate. In this case, the additional 0.10% in the stated rate produces a larger effect than the difference between quarterly and monthly compounding.

How to Recognize an EAR Question

EAR questions often include wording such as:

• Stated annual rate

• Quoted annual rate

• Nominal annual rate

• Compounded monthly, quarterly, or semiannually

• Effective annual rate

• Effective annual yield

• Compare rates with different compounding frequencies

When a question provides an annual rate and an intra-year compounding frequency, you will usually need to find the periodic rate before calculating the effective annual result.

Common Exam Traps

• Using the stated annual rate as the periodic rate.

• Dividing the rate by inline equation code while using a different exponent.

• Multiplying the periodic rate by inline equation code instead of compounding it.

• Forgetting to subtract 1 after raising the growth factor to the required power.

• Using 4 as inline equation code for semiannual compounding or 2 for quarterly compounding.

• Ranking investments from their stated rates before converting them to EAR.

• Assuming compounding frequency alone determines which option has the higher EAR.

• Using the multi-year exponent inline equation code when the question asks for a one-year EAR.

Practice Question

A deposit quotes a 10.80% stated annual rate compounded monthly. What is the effective annual rate?

1. 0.90%

2. 10.80%

3. 11.35%

FAQs About Effective Annual Rate