%
Enter a valid annual rate (0–100%).
Nominal annual rate (APR) before compounding
Select a frequency.
How often interest compounds per year
Periodic Rate
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⚠️ Disclaimer: This calculator converts nominal rates to periodic rates using the standard APR division method. Some financial products use different day-count conventions (360 vs 365 days). Always verify with your specific lender or institution.
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Sources & Methodology
Periodic rate formula verified against Investopedia financial reference library and Corporate Finance Institute (CFI) standards.
Investopedia — Periodic Interest Rate
Standard periodic rate definition, formula, and conversion methodology used in this calculator
Corporate Finance Institute — Interest Rate Calculations
EAR formula and compounding frequency comparison tables referenced for this calculator
Periodic Rate: r/n, where r = annual rate (decimal) and n = compounding periods per year. EAR: (1 + r/n)^n − 1. Interest on $1,000 per period: $1,000 × (r/n). The comparison table shows all standard compounding frequencies side by side for the entered annual rate.
⏱ Last reviewed: April 2026
How to Calculate Periodic Interest Rate
The periodic interest rate is the rate applied to a balance during each compounding period. It is derived from the nominal annual rate (APR) by dividing by the number of compounding periods per year. Knowing the periodic rate is essential for calculating loan payments, credit card interest, savings growth, and investment returns.
The Periodic Rate Formula
Periodic Rate = Annual Rate (r) / Number of Periods per Year (n)
Annual rate: 12% (0.12)
Monthly rate: 0.12 / 12 = 0.01 (1.0% per month)
Quarterly rate: 0.12 / 4 = 0.03 (3.0% per quarter)
Daily rate: 0.12 / 365 = 0.000329 (0.0329% per day)
Monthly rate: 0.12 / 12 = 0.01 (1.0% per month)
Quarterly rate: 0.12 / 4 = 0.03 (3.0% per quarter)
Daily rate: 0.12 / 365 = 0.000329 (0.0329% per day)
Periodic Rates for Common Annual Rates
| Annual Rate | Daily Rate | Monthly Rate | Quarterly Rate | EAR (Monthly) |
|---|---|---|---|---|
| 3% | 0.00822% | 0.250% | 0.750% | 3.042% |
| 6% | 0.01644% | 0.500% | 1.500% | 6.168% |
| 12% | 0.03288% | 1.000% | 3.000% | 12.683% |
| 18% | 0.04932% | 1.500% | 4.500% | 19.562% |
| 24% | 0.06575% | 2.000% | 6.000% | 26.824% |
Effective Annual Rate (EAR) vs Nominal Rate
The EAR accounts for the effect of compounding within the year: EAR = (1 + r/n)^n − 1. A 12% APR compounded monthly has an EAR of 12.683%. A credit card advertising "24% APR" with daily compounding actually costs 26.82% annually. The EAR is the true cost of borrowing or the true yield on investment — always compare financial products using EAR, not the stated nominal rate.
How Credit Cards Use Daily Periodic Rates
Credit cards calculate interest using the Daily Periodic Rate (DPR) = APR / 365. This DPR is applied to the average daily balance each day and summed over the billing cycle. For a $1,000 balance at 21% APR: DPR = 21/365 = 0.05753% per day. Over 30 days: interest = $1,000 × 0.0005753 × 30 = $17.26. The EAR at 21% APR daily compounding is 23.36% — significantly higher than the stated rate.
💡 Loan Payments Use Periodic Rate: The standard monthly loan payment formula is PMT = P × [i(1+i)^n] / [(1+i)^n − 1], where i = monthly periodic rate = APR/12. For a $200,000 mortgage at 6% APR for 30 years: i = 0.005, n = 360, PMT = $1,199.10/month. The monthly periodic rate (0.5%) is the critical input — not the annual rate directly.
Frequently Asked Questions
Periodic Rate = Annual Rate / Number of Periods per Year. For 12% annual compounded monthly: 12% / 12 = 1% per month. For daily: 12% / 365 = 0.03288% per day. The periodic rate is the actual rate applied to the balance each compounding period.
Monthly Rate = Annual Rate / 12. For 6% annual: 6/12 = 0.5% per month. In decimal: 0.06/12 = 0.005. This rate is used directly in loan payment formulas and compound interest calculations. The effective annual rate from 0.5% monthly compounding is (1.005)^12 − 1 = 6.168%, slightly above the 6% nominal rate.
The nominal rate is the stated annual rate (APR). The periodic rate is nominal / periods per year. For 12% APR: monthly = 1%, quarterly = 3%, daily = 0.0329%. The periodic rate is what is actually applied each period to calculate the interest charged or earned on a balance.
EAR = (1 + periodic rate)^n − 1. For 12% monthly: EAR = (1.01)^12 − 1 = 12.683%. EAR is the true annual yield after accounting for compounding. Always use EAR to compare loans or investments with different compounding frequencies — a 12% nominal rate can mean different true costs depending on how often it compounds.
Monthly rate = 24% / 12 = 2% per month. Credit cards often use daily compounding: daily rate = 24% / 365 = 0.06575% per day. The effective annual rate with daily compounding is (1 + 0.0006575)^365 − 1 = 27.11%. This is significantly higher than the stated 24% APR because of daily compounding.
Nominal Annual Rate = Periodic Rate × Number of Periods. If monthly rate is 0.75%: Annual = 0.75% × 12 = 9%. This gives the nominal rate. The effective annual rate (EAR) = (1 + 0.0075)^12 − 1 = 9.381% — higher than the 9% nominal due to monthly compounding.
Daily Periodic Rate = Annual Rate / 365 (or 360 for some lenders). For a 7% mortgage: 7% / 365 = 0.01918% per day. Used for per-diem interest in payoff calculations. Some lenders use 360 days: 7% / 360 = 0.01944% per day. Check your mortgage documents for the specific convention used.
Credit cards apply DPR = APR / 365 to the average daily balance each day, then multiply by days in the billing cycle. This results in slightly higher effective costs than monthly compounding. For 21% APR: DPR = 0.05753% per day; EAR = 23.36%. Regulators require APR disclosure, but EAR reflects actual cost.
Monthly payment: PMT = P × [i(1+i)^n] / [(1+i)^n − 1], where i = monthly rate (APR/12), n = months. For $200,000 at 6% for 30 years: i = 0.005, n = 360, PMT = $1,199.10. Increasing the monthly rate by 0.1% (to 0.6%/month = 7.2% APR) raises the payment to $1,306.68.
APY is already the EAR. To find monthly rate from APY: Monthly Rate = (1 + APY)^(1/12) − 1 = (1.045)^(1/12) − 1 = 0.3675%/month. If the account states APR, use APR/12 directly. APY is always the more meaningful number for savers as it reflects the true annual yield after compounding.
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