Effective Interest Rate Calculator

Two accounts can advertise the same annual interest rate and produce different one-year growth. The difference appears when interest is credited more than once: each credited amount can earn interest during the remaining periods. A quoted rate therefore needs its compounding schedule before it can be compared fairly.

A nominal annual rate states the rate parameter before within-year compounding. The effective annual rate (EAR) includes that compounding and expresses the resulting growth over one year. Annual, monthly, daily, custom-period, and continuous quotes become comparable only after each is converted on its own basis.

More frequent compounding raises EAR when the nominal rate is positive, although the difference may be only a few basis points. One basis point is 0.01 percentage point. A small compounding advantage can be outweighed by an account fee, a minimum balance, a withdrawal penalty, credit risk, tax treatment, or a promotional rate that later changes.

Holding-period return answers a narrower timing question: what fixed annual effective rate implies over a selected number of days. It does not model the account's actual day-count convention, cash-flow timing, tiered balances, or early withdrawal terms. Real return is equally assumption-dependent because it uses the inflation rate supplied by the reader.

EAR is a normalization measure, not a recommendation. Read the product disclosure for how interest is calculated and credited, then compare liquidity, guarantees, fees, taxes, and contractual restrictions alongside the annualized yield.

How to Use This Tool:

Start from the stated nominal annual rate and the compounding basis shown in the same disclosure.

1. Enter Quoted nominal rate in percent form, such as 5 for 5% per year.
2. Choose Compounding basis. Select custom only when the quote names a discrete schedule outside the standard annual, semiannual, quarterly, monthly, weekly, or daily choices.
3. Open Advanced to compare a second nominal quote. Give that quote its own basis so both offers are converted to EAR before the spread is calculated.
4. Set an Equivalent quote basis when you need the nominal quote that preserves the current EAR on another schedule. Add inflation or a holding horizon only when those assumptions answer a real planning question.
5. Read Yield Audit for the normalized rate and Offer Check for a like-for-like comparison. Recheck any normalization note before using the result.

Interpreting Results:

Effective annual rate is the main comparison value. Compare EAR with EAR, not an EAR from one offer with a nominal quote from another. Compounding lift shows the difference between EAR and the stated nominal rate in basis points.

• A positive spread means the current quote has the higher EAR under the entered schedules; a negative spread favors the comparison quote.
• Equivalent nominal rate changes the quote basis without changing the one-year growth represented by the EAR.
• Holding return assumes the same effective annual growth for the selected number of days using a 365-day year.
• Real effective rate can be negative even when EAR is positive if the inflation assumption is higher than the investment return.

A higher EAR does not establish the better product. Verify fees, rate guarantees, balance tiers, compounding and crediting rules, withdrawal conditions, and the institution's disclosure before acting on a narrow spread.

Technical Details:

Effective-rate conversion treats the quoted annual percentage as a fixed rate parameter. Discrete compounding divides it among a whole number of periods; continuous compounding uses the exponential limit. The calculations retain full precision and round only for display.

Formula Core:

The first equation converts a nominal quote to EAR. The remaining equations reverse the quote basis or derive the optional planning values.

r_nom is the nominal annual rate as a decimal, m is discrete compounding periods per year, r_eff is EAR, d is holding days, and π is the annual inflation assumption. A continuous equivalent nominal quote is ln(1 + r_eff), and estimated doubling time is ln(2) ÷ ln(1 + r_eff).

A 5% nominal quote compounded monthly produces an EAR of about 5.1162%. The compounding lift is about 11.62 basis points, a 180-day holding return is about 2.4912%, and the implied doubling time is about 13.89 years if that effective rate remains fixed.

The second quote is converted independently on its selected basis before the EAR spread is taken. Choosing a new equivalent basis changes only the reverse nominal quote; it does not alter the current EAR.

Financial Limits:

This is an educational fixed-rate comparison, not financial advice or a regulated product disclosure calculation.

• Tiered, stepped, variable, promotional, and fee-bearing products may require cash-flow and balance rules that a single nominal quote cannot represent.
• Holding return uses a 365-day year and does not reproduce every institution's accrual, crediting, leap-year, or withdrawal convention.
• Inflation and doubling-time values assume a constant rate; neither is a forecast or guarantee.

References:

• Appendix A to Part 1030: Annual Percentage Yield Calculation, Consumer Financial Protection Bureau.
• How does compound interest work?, Consumer Financial Protection Bureau, October 19, 2023.
• Compound Interest, Investor.gov.