APR to EAR Converter
Convert APR (Annual Percentage Rate) to EAR (Effective Annual Rate). Understand true cost of loans and credit cards.
Reviewed by the Calcura editorial team · Last reviewed
- Question
- How do I convert APR to EAR?
- Answer
- EAR = (1 + APR/n)ⁿ − 1, where n is the number of compounding periods per year. A 12% APR compounded monthly (n=12) works out to (1 + 0.01)¹² − 1 = 12.68% EAR. The more often a rate compounds, the higher the true annual cost — so a credit card at 18% APR compounding daily has an EAR closer to 19.7%. Use EAR (also called APY on deposits) for apples-to-apples comparisons.
▸Show formula & caveatsHide formula & caveats
- Formula
EAR = (1 + APR/n)ⁿ − 1- Caveats
- APR and EAR only differ when the rate compounds more than once per year.
- Continuous compounding uses EAR = eᴬᴾᴿ − 1 as the limit of the formula.
- Credit-card APRs typically compound daily; savings APYs typically compound daily or monthly.
What This Calculator Does
This tool converts a stated APR (annual percentage rate) to an EAR (effective annual rate, also called APY for deposit products). The difference matters because APR is a simple annual rate that ignores intra-year compounding, while EAR captures the actual yield or cost once compounding is factored in. For a credit card at 18% APR that compounds daily, the EAR is closer to 19.7% — you actually pay ~1.7 percentage points more than the APR implies. The calculator uses the standard formula EAR = (1 + APR/n)^n − 1, where n is the number of compounding periods per year.
When To Use This Calculator
Comparing credit cards or loans with different compounding periods
Card A quotes 17.99% APR with monthly compounding and Card B quotes 18.25% APR with annual compounding. Convert both to EAR (≈19.56% vs 18.25%) and Card B is actually cheaper despite the higher advertised rate.
Shopping a savings account or CD
One bank offers 4.50% APR compounded monthly (APY ≈ 4.59%). Another offers 4.45% APR compounded daily (APY ≈ 4.55%). The first pays more — the difference in compounding frequency does not fully offset the lower stated rate.
Sanity-checking a lender's disclosure
A lender discloses only APR. If the product compounds daily or monthly, calculating the EAR shows what you actually owe annually. This is useful when comparing a mortgage or personal loan against a line of credit that compounds more frequently.
Converting between APR and APY to compare apples to apples
Deposit products are required to quote APY (= EAR); loan products quote APR. To compare a savings account's 4.5% APY against a bond paying 4.5% APR compounded semi-annually, convert the APR to its EAR (~4.55%) for a like-for-like comparison.
How It Works
EAR re-expresses a nominal annual rate in a way that accounts for compounding. Start with APR divided by the number of compounding periods per year (n) — that's the periodic rate. Add 1, raise to the n-th power, and subtract 1. The result is the effective one-year growth factor minus 1 — the actual percentage your balance grows by (or your loan costs) over a full year if every period's interest compounds forward. Annual compounding gives EAR = APR exactly; more frequent compounding widens the gap, with continuous compounding producing EAR = e^APR − 1 as the upper bound.
Formula
EAR = (1 + APR / n)^n − 1Real-World Example
Scenario
A credit card advertises 24.99% APR and compounds interest daily (n = 365). You want to know the effective annual cost on a $5,000 revolving balance.
Calculation
Periodic rate: 24.99% ÷ 365 ≈ 0.0685% per day EAR: (1 + 0.2499/365)^365 − 1 ≈ 0.2839, or 28.39% Applied to $5,000: $5,000 × 0.2839 ≈ $1,420 in annual interest if the balance is held flat
Result
The advertised 24.99% APR corresponds to a 28.39% EAR. On a $5,000 balance carried for a year, that's about $170 more than the APR alone would suggest — a real difference worth factoring into any plan to pay down revolving debt.
Common Mistakes to Avoid
Mistake: Comparing APR to APY directly
Solution: APR and APY (EAR) are different quantities. A 5.00% APR compounded monthly is a 5.12% APY. Always convert to the same measure — EAR/APY is the honest comparison for both sides.
Mistake: Assuming APR is the annual cost of a loan
Solution: APR is the nominal rate; your actual interest cost depends on compounding frequency and any fees. For a credit card or line of credit that compounds daily, EAR is meaningfully higher — use it as your real-cost estimate.
Mistake: Ignoring fees when comparing rates
Solution: EAR captures compounding but not origination fees, annual fees, or prepayment penalties. For a loan, the lender's disclosed APR (under Regulation Z) already folds many fees into the rate; for deposits, fees are disclosed separately. Read the full cost disclosure, not just the rate.
Mistake: Using continuous compounding as a default
Solution: Real-world products compound daily, monthly, or quarterly — not continuously. e^APR − 1 is the upper bound for EAR, but it overstates the real rate unless the contract truly compounds continuously (rare outside of certain derivatives).
APR vs. EAR: Related Calculators
Compound Interest Calculator
Project the actual dollar growth of a balance at a given rate and compounding frequency. Use this when you need the end value, not just the effective rate.
Simple Interest Calculator
For loans that charge simple interest (no compounding), APR equals EAR. Use this for short-term notes or certain auto loans.
Loan Payment Calculator
Once you know the effective rate, this tool returns the monthly payment for a given loan size and term.
When This Isn't the Right Tool
Adjustable-rate or variable-rate products
Use instead: APR-to-EAR conversion assumes a fixed rate. For ARMs, HELOCs, or variable credit lines, compute EAR separately for each rate regime — or use the lender's worst-case disclosure.
Products with fees rolled into the APR
Use instead: Regulation Z APR on closed-end loans includes certain fees. Converting that APR to EAR overstates the pure interest-rate cost, since part of the APR reflects amortized fees rather than compounding interest.
Tax-adjusted yield comparisons
Use instead: Comparing a taxable savings APY to a tax-exempt municipal bond requires an after-tax adjustment. EAR alone doesn't capture the tax treatment — use a tax-equivalent yield calculation first.
Products with irregular compounding
Use instead: Some contracts compound on calendar days including weekends; others skip weekends; others use 360-day years. For exact figures, model the actual accrual convention in a spreadsheet rather than relying on a generic EAR formula.
How to Verify This Calculation
In Excel or Google Sheets, =EFFECT(apr, n) returns the EAR for a nominal APR with n compounding periods per year. Cross-check a simple case: 12% APR compounded monthly should return ~12.68% EAR; annually compounded, it returns exactly 12.00%.
Sources
- Consumer Financial Protection Bureau — APR explainer — Plain-language CFPB guide to APR and how it differs from the stated interest rate.
- Federal Reserve — Regulation Z (Truth in Lending Act) — Rules governing APR disclosure for consumer credit products.
- FDIC — Regulation DD (Truth in Savings) — Rules requiring APY (= EAR) disclosure for U.S. deposit accounts.
Reviewed by the Calcura editorial team · Last reviewed