EAR vs APR Formula: Convert APR to EAR Step-by-Step
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EAR vs APR Formula: Convert APR to EAR Step-by-Step
The EAR vs APR formula is one line: EAR = (1 + APR ÷ m)m − 1, where m is the number of compounding periods per year. APR is the quoted (nominal) rate that ignores compounding; EAR is what you actually pay or earn once compounding is counted. Whenever m > 1, EAR is higher than APR.
APR vs periodic vs EAR — what’s the difference?
| Rate | What it is | Example (18% / monthly) |
|---|---|---|
| APR (nominal) | Quoted yearly rate, ignores compounding | 18% |
| Periodic | APR ÷ m — the rate per compounding period | 18% ÷ 12 = 1.5% / month |
| EAR (effective) | True annual rate after compounding | 19.56% |
How do you convert APR to EAR? (worked example)
A credit card quotes an 18% APR, compounded monthly. What’s the EAR?
Find the periodic rate. 18% ÷ 12 = 1.5% per month.
Compound over the year. (1 + 0.015)12 = 1.19562.
Subtract 1. 1.19562 − 1 = 0.19562 → EAR ≈ 19.56%.
So an “18%” card really costs 19.56% a year. The more frequent the compounding, the bigger the gap between APR and EAR.
On the BA II Plus (ICONV worksheet)
| Press | Display | Why |
|---|---|---|
| 2ND → ICONV | NOM = | open the interest-conversion worksheet |
| 18 → ENTER | NOM = 18 | the nominal rate (APR) |
| ↓ ↓ → 12 → ENTER | C/Y = 12 | compounding periods per year |
| ↑ → CPT | EFF = 19.56 | the effective annual rate |
Rates and compounding tripping you up? A tutor can drill APR, EAR and periodic conversions until they’re automatic — book a session.
The mistake to avoid
Don’t plug an annual APR into a TVM problem that compounds monthly. Either convert the rate to periodic and match N to months, or convert to EAR first — mixing the two is the most common reason answers come out wrong. The same trap appears with BA II Plus TVM problems when P/Y and the rate don’t match.
Frequently asked questions
How do you convert APR to EAR?
Divide the APR by the number of compounding periods (m) to get the periodic rate, raise (1 + periodic) to the power m, and subtract 1: EAR = (1 + APR/m)m − 1.
Is EAR always higher than APR?
Yes, whenever interest compounds more than once a year. If compounding is annual (m = 1), EAR equals APR.
What is the periodic rate?
The interest rate for a single compounding period — APR divided by m. It’s the rate you actually use inside time-value-of-money calculations.
When should I use EAR instead of APR?
Use EAR to compare options with different compounding frequencies; use the periodic rate inside the actual TVM math.
Finance midterm on interest rates?
Book 1-on-1 tutoring on TVM, APR/EAR and the BA II Plus — worked with your own course problems.
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