Effective Interest Rate

1. Enter the **nominal interest rate** (the stated rate, e.g., 6%) in the first field.
2. Select or enter the **compounding frequency** — how many times per year interest is compounded (e.g., monthly = 12, quarterly = 4, daily = 365).
3. Click **Calculate** to instantly see the **Effective Annual Rate (EAR)** as a percentage.
4. Compare the EAR with the nominal rate to understand how much extra interest compounding adds over a year.
5. Use the result to compare multiple financial products that may advertise different nominal rates or compounding schedules.

EAR = (1 + r/n)^n − 1

• EAR — Effective Annual Rate — the true annual interest rate after compounding, expressed as a decimal (multiply by 100 for a percentage).
• r — Nominal interest rate — the stated or advertised annual interest rate, expressed as a decimal (e.g., 6% → 0.06).
• n — Number of compounding periods per year (e.g., 12 for monthly, 4 for quarterly, 2 for semi-annual, 365 for daily, 1 for annual).

EAR = (1 + 0.06/12)^12 − 1 = (1 + 0.005)^12 − 1 = (1.005)^12 − 1 = 1.061677812 − 1 = 0.061677812

Result: EAR ≈ 6.17%

A nominal rate of 6% compounded monthly produces an Effective Annual Rate of 6.17%. This means that for every $1,000 deposited or borrowed, you actually earn or owe $61.68 in interest over one year — not $60.00 as the nominal rate might imply. The extra $1.68 comes from compounding: each month's interest begins earning interest itself. The higher the compounding frequency, the larger the gap between the nominal and effective rates. Note: Results are estimates for educational comparison. Actual rates from a bank or lender may differ due to fees, rounding conventions, or specific product terms.

Nominal Rate vs. Effective Annual Rate

When a bank or lender advertises an interest rate, they typically quote the nominal rate (also called the Annual Percentage Rate or APR in some contexts). This is the rate before compounding is applied. The Effective Annual Rate (EAR), sometimes called the Annual Equivalent Rate (AER), reflects what you actually earn or pay once compounding is factored in.

Why Compounding Frequency Matters

The same nominal rate produces different effective rates depending on how often interest is compounded:

| Compounding Frequency | n | EAR (at 6% nominal) | |---|---|---| | Annually | 1 | 6.000% | | Semi-annually | 2 | 6.090% | | Quarterly | 4 | 6.136% | | Monthly | 12 | 6.168% | | Daily | 365 | 6.183% | | Continuously | ∞ | 6.184% |

Continuous Compounding

In the limit where compounding occurs infinitely often, the EAR formula becomes:

EAR = e^r − 1

where e ≈ 2.71828. For r = 6%, this gives EAR = e^0.06 − 1 ≈ 6.184%.

Practical Applications

• Savings accounts & CDs: Banks often advertise a nominal APY (Annual Percentage Yield) that already reflects compounding. Confirming the EAR helps you verify the advertised APY.
• Credit cards: Many cards compound daily. A nominal rate of 20% compounded daily gives an EAR of about 22.13% — significantly higher.
• Mortgages and loans: In many countries, lenders must disclose an APR that includes fees, but the compounding convention varies. Converting to EAR ensures fair comparison.
• Investing: When evaluating bond yields or investment returns quoted at different compounding intervals, converting to EAR creates a consistent basis for comparison.

Key Takeaway

Always compare financial products using the EAR rather than the nominal rate. The EAR is the single most honest measure of what you will actually earn or owe over one year.

• **Entering the rate as a whole number instead of a percentage** — if your calculator expects a decimal, enter 0.06 for 6%, not 6.
• **Using the wrong compounding frequency** — monthly billing does not always mean monthly compounding; always verify the product's terms.
• **Confusing APR with EAR** — in the US, APR for mortgages includes fees and uses a specific legal definition; it is not the same as EAR.
• **Ignoring fees and charges** — the EAR formula only accounts for compounding; origination fees, service charges, or points are not included and can raise the true cost further.
• **Assuming continuous compounding** — while theoretically elegant, most real-world products compound daily, monthly, or quarterly, not continuously.
• **Comparing EAR to a simple interest rate** — simple interest products do not compound, so a 6% simple interest rate is already its own 'effective' rate; do not run it through the EAR formula.

• Truth in Savings Act — Annual Percentage Yield Calculation — Consumer Financial Protection Bureau (CFPB) / Electronic Code of Federal Regulations
• Principles of Corporate Finance — Interest Rate Compounding Conventions — McGraw-Hill Education (Brealey, Myers & Allen)
• Time Value of Money — Interest Rate Conversions — Khan Academy
• CFA Program Curriculum — Time Value of Money — CFA Institute

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