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Effective Interest Rate Calculator

Convert nominal APR to an effective annual rate (EAR/EIR/APY) for monthly, daily, custom, or continuous compounding. You can also reverse the calculation to find an equivalent nominal APR.

Calculate EAR / Effective Annual Rate

Enter 6 for 6%. Negative rates are allowed above the mathematical lower limit.

Compounding Frequency Comparison

For nominal APR input, this table shows how the same quoted annual rate changes as compounding becomes more frequent. For effective-rate input, it shows equivalent nominal APRs.

Compounding Periods/year Effective annual rate Equivalent nominal APR Periodic rate

Formulas and Assumptions

Effective annual rate = (1 + r / m)^m - 1
Equivalent nominal APR = m * ((1 + EAR)^(1 / m) - 1)
Continuous compounding: EAR = e^r - 1, APR = ln(1 + EAR)

Here r is the nominal annual rate as a decimal and m is the number of compounding periods per year. The projection assumes the effective annual rate applies evenly over full and fractional years, with no fees, taxes, promotional rate changes, deposits, withdrawals, or lender-specific day-count conventions beyond the selected frequency.

Use the comparison table when two quoted rates look similar but compound on different schedules. Monthly, daily, and continuous compounding can produce different annual outcomes even when the headline APR is the same. For savings products, the effective rate is useful for comparing growth. For borrowing, it helps show the annualized cost of compounding before adding fees or payment timing.

Financial products can define and disclose rates under jurisdiction-specific rules. Use this as an educational calculator, not financial advice or a replacement for the product's official disclosure.

FAQs

What does effective interest rate mean?

The effective annual interest rate is the annual rate after compounding is included. It lets you compare rates with different compounding schedules on a like-for-like annual basis.

How is this different from APR?

APR is usually a nominal annual rate. If interest compounds during the year, the effective annual rate is generally higher than the APR for positive rates.

Can I use this for loans and savings accounts?

Yes for basic rate conversion. For real loan or deposit decisions, also account for fees, payment timing, taxes, minimum balances, grace periods, and local disclosure rules.

Why include daily 360 and daily 365?

Some finance contexts use a 360-day year while others use 365. The selected frequency changes the math, so both options are included for transparent comparisons.

What should I check before relying on a quoted rate?

Check whether the rate is nominal or effective, how often interest compounds, whether fees are included, and whether the rate can change over time. Loan disclosures, bank terms, and investment documents may use similar labels for different calculations.

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