Effective Interest Rate Calculator
From the nominal annual rate and compounding frequency, compute the effective interest rate (EIR) and the periodic rate.
Input Data
Results
At a glance:The Effective Interest Rate (EIR) converts the nominal annual rate by compounding frequency into the real annual rate that includes compounding — the same concept as EAR and APY. Discrete: EIR = (1 + r/m)^m − 1; continuous: EIR = e^r − 1. EIR is the fair basis when comparing loan costs or deposit returns at different compounding frequencies.
Formula
EIR = (1 + r/m)^m − 1, where r is nominal annual rate, m is compounds per year.
Continuous compounding: EIR = e^r − 1.
Periodic rate = r ÷ m (continuous has no single periodic rate, shown as 0).
$$$EIR = \\left(1+\\dfrac{r}{m}\\right)^{m}-1$$$$$$EIR = e^{r}-1$$$$$(18%)$\\left(1+\\frac{0.18}{12}\\right)^{12}-1\\approx19.56\\%$$$How to Use
- Enter the nominal annual rate quoted by the bank or loan.
- Select the compounding frequency (continuous optional).
- Get the effective rate (EIR) and periodic rate instantly.
EIR at common nominal rates and frequencies
| Nominal rate | Frequency | Effective rate (EIR) | Context |
|---|---|---|---|
| 12% | Monthly | 12.6825% | General loan |
| 18% | Monthly | 19.5618% | Credit-card revolving |
| 24% | Daily | 27.1149% | High-rate small loan |
Case Studies
Case 1: True cost of credit-card revolving interest
A credit card shows an annual (nominal) rate of 18%, compounded monthly (m = 12).
EIR = (1 + 0.18/12)^12 − 1 = (1.015)^12 − 1 ≈ 19.5618%.
Interpretation: though nominal 18%, because unpaid balances accrue interest monthly and that interest compounds, the real annual rate is about 19.56%, over 1.5 points above nominal. This shows why clearing the card balance each period and avoiding revolving credit is sound.
Case 2: Same nominal, different compounding, different cost
Compare two loans both nominal 12%: loan A compounded monthly, EIR = (1 + 0.12/12)^12 − 1 ≈ 12.68%; a daily-compounded variant would be higher; a nominal 24% daily loan reaches about 27.11% EIR.
By nominal rate alone (both '12%') you would think costs match, but after compounding the real cost (EIR) differs.
Interpretation: always check the compounding behind the nominal rate and convert to EIR before comparing. Same nominal does not mean same cost; a lower nominal but more frequent compounding may not be cheaper. EIR uniformly counts compounding — the right tool. Actual total cost should also include fees (APR); this calculator covers compounding only.
FAQ
How does EIR differ from the nominal annual rate?
The nominal rate just multiplies the periodic rate by the number of periods, ignoring compounding. EIR reflects interest rolling into principal and earning interest again — the true annual return. The more frequent the compounding, the higher the EIR above the nominal rate.
Why compare loans by EIR?
Loans compound at different frequencies; the nominal rate alone understates the real cost. Converting to EIR on an annual basis lets you compare loans and deposits fairly.
How is continuous-compounding EIR computed?
As compounding frequency tends to infinity, EIR's limit is e^r − 1 (e is the natural constant). This is the highest EIR for a given nominal rate across all frequencies.
Why must I look at EIR, not the nominal rate, when comparing loans?
Because the nominal rate understates the true cost — only EIR reflects the actual annual rate you pay, which protects borrowers. Two reasons: (1) compounding — the nominal rate ignores interest rolling into principal and compounding again; many loans (especially credit-card revolving credit) compound monthly or daily, so the actual rate exceeds the nominal. A nominal 18% compounded monthly is really about 19.56%. (2) different compounding methods — two loans at the same nominal rate but different frequencies have different real costs; the nominal number alone cannot compare them. Also, real borrowing adds fees (handling, origination, insurance); the all-in annualised cost (APR in some regions) is closest to true cost. This calculator's EIR covers the compounding layer — already better than the nominal rate — but for major borrowing also count fees to see the true annual rate. Nominal is the headline; EIR is the real rate — compare by the latter.
Is EIR the same as EAR and APY?
Mathematically EIR, EAR and APY are the same concept with the identical formula: discrete (1 + r/m)^m − 1, continuous e^r − 1. The difference is only naming and context. APY is used for deposits/savings (you earn) — higher is better for savers. EAR is the general term across deposits, loans and investing. EIR is used for loans/borrowing cost — higher is worse for borrowers. Same formula, same number; called APY in an earnings context, EAR/EIR in a cost/general context. Do not confuse with the nominal APR, which excludes compounding and is usually lower. So the 'effective rate' this calculator shows is also the equal EAR and APY — pick the familiar name by context.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.