Converter Inputs
How to Use This Calculator
- Enter the interest rate value and select its unit.
- Choose the input type that matches how the rate is quoted.
- Select the input frequency if the quote depends on compounding.
- Pick the desired output type and output frequency if needed.
- Set display unit and decimals, then convert the rate.
Formulas Used
This converter first transforms your input into an effective annual rate (EAR), then derives the requested output from that EAR.
| Conversion | Formula |
|---|---|
| Nominal APR → EAR | EAR = (1 + APR/m)m − 1 |
| Periodic rate → EAR | EAR = (1 + rp)m − 1 |
| EAR → Nominal APR | APR = m · ((1 + EAR)1/m − 1) |
| EAR → Periodic rate | rp = (1 + EAR)1/m − 1 |
| Continuous ↔ EAR | EAR = erc − 1 and rc = ln(1 + EAR) |
Here, m is the number of compounding periods per year.
Example Data Table
Sample conversions for common rate quotes (illustrative only).
| Scenario | Quoted Rate | Quote Type | Approx. EAR | Monthly Periodic |
|---|---|---|---|---|
| Credit APR, monthly comp | 12.00% | Nominal APR, m=12 | 12.6825% | 1.0000% |
| Savings APY quote | 4.50% | Effective annual | 4.5000% | 0.3660% |
| Quarterly periodic promo | 1.20% | Periodic, m=4 | 4.8865% | 0.3984% |
| Continuous discounting | 3.80% | Continuous | 3.8735% | 0.3172% |
| Daily comp bank rate | 5.25% | Nominal APR, m=365 | 5.3932% | 0.4391% |
For precise reporting, always use your institution’s stated basis.
Why Rate Formats Differ
Interest-rate quotes differ because each quote embeds a compounding rule. The converter standardizes every input into an effective annual rate (EAR), then rebuilds the output format. This lets you compare offers where one lender states a nominal APR with monthly compounding (m=12) and another publishes an annual yield (m=1).
Impact of Compounding Frequency
Compounding frequency drives the gap between a stated APR and true annual growth. A 12.00% nominal APR compounded monthly implies an EAR near 12.6825%, while the same APR compounded daily on a 365-day basis is slightly higher. Weekly (52), biweekly (26), quarterly (4), and semiannual (2) are common settings in lending and deposits.
Periodic Rates for Payment Schedules
Periodic rates matter for cash-flow models. If you know the per-period rate r_p, the annual effect is (1+r_p)m−1. A quarterly periodic rate of 1.20% converts to an EAR near 4.8865%, and the equivalent monthly periodic rate is roughly 0.3984%. This helps align payment schedules, discounting, and budgeting using consistent time steps.
Continuous Rates in Valuation
Continuous compounding appears in valuation and theoretical discounting. It uses r_c where EAR = erc−1. A continuous rate of 3.80% corresponds to an EAR around 3.8735%. Because continuous compounding is smooth, it is convenient for log returns, forward-rate math, and models that assume infinitely frequent compounding.
Day-Count Basis and Reporting Controls
Operational conventions also influence results. Many money-market calculations use a 360-day year, while many bank and bond conventions use 365. The calculator includes both daily bases so you can mirror the quote you received. Record the selected basis, frequency, and rounding (0–10 decimals) for consistent audit trails.
Practical checks improve reliability. Convert the quoted rate to several outputs (APR, periodic, continuous) and verify that the computed EAR stays constant across rows in the results table. If you are comparing products with fees, teaser periods, or variable rates, translate those cash flows to an internal rate of return; a single headline rate may mislead. For negative yields, ensure 1+rate remains positive for logarithms.
FAQs
1) What is the difference between nominal APR and EAR?
Nominal APR states an annual rate without showing compounding impact. EAR includes compounding, so it reflects the true annual growth or cost. Equal APRs can produce different EARs when compounding frequencies differ.
2) When should I change the periods per year?
Match the frequency used in the quoted product. Use monthly for most credit cards and installment loans, daily for many savings accounts, and quarterly or semiannual for specific contracts. The correct m keeps comparisons fair.
3) What does the continuous rate represent?
It is an annualized rate used with continuous compounding. The converter maps it to EAR using exponential growth and maps EAR back using a natural logarithm. It is common in pricing, term-structure, and log-return work.
4) How does the custom frequency option help?
Custom periods per year lets you mirror nonstandard schedules, such as 24 periods for semi-monthly, 48 for four-week cycles, or bespoke accrual calendars. Use it when your contract defines compounding beyond standard presets.
5) Should I display results as percent or decimal?
Use percent for reports and stakeholder reviews, and decimal for spreadsheet formulas and models. A 12% rate equals 0.12 in decimal. Consistent units prevent copy-paste errors when applying the rate elsewhere.
6) What do the CSV and PDF downloads include?
Downloads capture your input settings, the converted output, and the common-frequency comparison table. This creates a portable record for audits, underwriting notes, and planning documents, without re-running calculations later.