Monthly compounding
- Nominal APR 6%, periods 12.
- EAR ≈ (1 + 0.06/12)^12 − 1 ≈ 6.17%. Monthly equivalent ≈ 0.5%.
finance calculator
Nominal vs Effective Interest Rate
Convert a nominal APR with compounding periods into an effective annual rate and equivalent monthly rate.
Results
- Effective annual rate (EAR)
- 6.17%
- Equivalent monthly rate
- 0.50%
How to use this calculator
- Enter nominal APR and compounding periods per year.
- We compute the effective annual rate and the equivalent monthly rate.
- Adjust periods per year (e.g., 12 vs 365) to see how compounding changes the effective rate.
Inputs explained
- Compounding periods
- Number of times interest compounds per year (12 for monthly, 365 for daily, etc.).
- Nominal APR (%)
- The stated annual percentage rate before compounding effects.
How it works
EAR = (1 + nominal / periods)^periods − 1.
Monthly equivalent = (1 + EAR)^(1/12) − 1.
Formula
EAR = (1 + nominalRate/periodsPerYear)^(periodsPerYear) − 1. Monthly equivalent = (1 + EAR)^(1/12) − 1.
When to use it
- Comparing loans or investments with different compounding frequencies.
- Converting APR to EAR for apples-to-apples comparisons.
- Finding a monthly rate for budgeting or payment estimates.
- Checking how daily vs monthly compounding affects savings account returns.
- Estimating true borrowing cost when fees are quoted as nominal APR with specific compounding.
Tips & cautions
- Use 365 for daily compounding, 52 for weekly, 12 for monthly.
- EAR will be higher than nominal when compounding more than once per year.
- For simple-interest products (no intra-year compounding), periods may effectively be 1.
- When comparing credit cards, know if APR assumes daily compounding on average daily balance.
- Assumes fixed nominal rate and regular compounding; does not model fees.
- Does not include APR calculation nuances with fees/points; input the APR as provided.
- Does not handle continuously compounding explicitly—use a high period count to approximate.
Worked examples
Daily compounding
- Nominal APR 6%, periods 365.
- EAR ≈ (1 + 0.06/365)^365 − 1 ≈ 6.18%.
- Daily compounding slightly increases the effective rate vs monthly.
Weekly compounding comparison
- Nominal APR 5%, periods 52.
- EAR ≈ (1 + 0.05/52)^52 − 1 ≈ 5.12%. Monthly equivalent ≈ 0.417%.
Deep dive
Convert nominal APR to effective annual rate with custom compounding periods and see the equivalent monthly rate.
Enter nominal rate and compounding frequency to compare APR vs EAR for loans or investments.
Test daily, weekly, or monthly compounding to see how it changes effective yield or cost.
Use the equivalent monthly rate for budgeting or payment estimates with consistent compounding assumptions.
FAQs
- How do I approximate continuous compounding?
- Use a very high periods-per-year value (e.g., 10,000) to approximate e^(nominal) − 1, though this tool doesn’t explicitly model continuous compounding.
- Does this account for fees or APR calculation quirks?
- No. Enter the nominal APR as provided. If fees change the true APR, adjust the nominal input or use a lender-provided APR.
- Can I use this for savings APY?
- Yes. APY is an effective rate; you can input the nominal and compounding to see EAR and compare to stated APY.
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Simplified nominal-to-effective converter. Ignores fees, assumes regular compounding, and does not model continuous compounding exactly. Use lender-quoted APR/compounding details for accurate comparisons. Not financial advice.