Effective Annual Rate (EAR) Calculator
The EAR (also called APY) is the true annual rate after compounding. The nominal rate is what ads show; the EAR is what lets you compare loans, cards, and deposits fairly.
With 12% nominal and monthly compounding (n = 12):
- EAR = 12.682503% (~12.68%)
- Period rate = 1% per month
- Monthly equivalent = 1%
- Daily equivalent ≈ 0.032719%
A bank advertising 12% nominal with monthly compounding actually costs or yields 12.68% per year, not 12%.
Formula
EAR = (1 + r/n)^n − 1
where: r = nominal annual rate as a decimal (12% → 0.12) n = compounding periods per year (monthly = 12, daily = 365, annual = 1)
Period rate = r / n Monthly equivalent = (1 + EAR)^(1/12) − 1
Step-by-step example (defaults)
- r = 0.12 · n = 12
- Period rate = 0.12 / 12 = 0.01 (1%)
- EAR = (1.01)^12 − 1 = 0.12682503 → 12.682503%
- Monthly equivalent from EAR: (1.12682503)^(1/12) − 1 = 1%
Scenario table (monthly compounding)
Engine values (EAR to 6 decimal places).
| Nominal | EAR | Period rate | Monthly equiv. |
|---|---|---|---|
| 6% | 6.167781% | 0.5% | 0.5% |
| 10% | 10.471307% | 0.833333% | 0.833333% |
| 12% | 12.682503% | 1% | 1% |
| 15% | 16.075452% | 1.25% | 1.25% |
| 18% | 19.561817% | 1.5% | 1.5% |
| 24% | 26.824179% | 2% | 2% |
| 36% | 42.576089% | 3% | 3% |
| 42% | 51.106866% | 3.5% | 3.5% |
A card at 42% nominal monthly is not “42% a year”: EAR rises to ~51.11%. Also use the credit card payment and debt payoff tools.
Same 12% nominal: frequency changes EAR
| Frequency | n | EAR | Period rate |
|---|---|---|---|
| Daily | 365 | 12.747462% | 0.032877% |
| Weekly | 52 | 12.734099% | 0.230769% |
| Monthly | 12 | 12.682503% | 1% |
| Quarterly | 4 | 12.550881% | 3% |
| Semi-annual | 2 | 12.36% | 6% |
| Annual | 1 | 12% | 12% |
Higher frequency → higher EAR for the same nominal rate. Daily vs monthly at 12% is a small gap (~0.06 pp); annual vs daily is ~0.75 pp.
Nominal vs EAR
| Feature | Nominal rate | EAR |
|---|---|---|
| What it is | Advertised rate | True rate with compounding |
| Compounding | Not included | Included |
| Comparing products | Misleading if n differs | Fair comparison |
| Typical use | Marketing | Decision analysis |
Golden rule: always compare EAR/APY (or full APR disclosures with fees), not nominal alone.
Using the EAR with loans
- Convert the lender’s nominal rate to EAR here.
- Project payments with the personal loan and amortization calculators.
- For extra payments: early loan payoff.
- For savings growth: compound interest and simple interest.
FAQ
It is the true annual rate after compounding. With 12% nominal monthly, EAR is 12.682503% (~12.68%).
EAR = (1 + r/n)^n − 1. With n = 12 and r = 12%: (1.01)^12 − 1 = 12.682503%.
Because interest is added to principal and earns interest. Only when n = 1 (annual compounding) does EAR equal the nominal rate.
Yes in concept: APY (Annual Percentage Yield) is the same idea as EAR with compounding.
Not necessarily. With monthly compounding, 42% nominal → EAR 51.106866%. Fees can raise the true APR further.
No. It only models compounding. Total credit cost can be higher.
12% nominal and monthly compounding → EAR 12.682503%, period rate 1%, monthly equivalent 1%.
Related calculators
- Compound interest
- Simple interest
- Personal loan
- Amortization schedule
- Early loan payoff
- Credit card payment
- Debt payoff
- Debt-to-income ratio
Educational compounding estimate only. Does not include fees, insurance, taxes, or a full APR disclosure. Confirm the effective rate and total cost with your lender.