Interest rate applied during one defined accrual, billing, payment, or compounding period such as a day, month, or quarter.
A periodic interest rate is the rate applied for one defined interest period, such as a day, month, quarter, or six-month interval. It is the rate actually multiplied by a balance or used in a compounding factor for that period. Its conversion from an annual rate depends on whether the annual rate is nominal or effective and on the product’s day-count, balance, and compounding rules.
If a contract quotes a nominal annual rate \(r_{nom}\) convertible \(m\) equal times per year, the periodic rate is:
For a 12% nominal annual rate compounded monthly:
The resulting effective annual rate is not 12% because twelve 1% periods compound:
This division rule is valid because the 12% quote was defined as nominal and the periods were equal. It should not be applied automatically to an EAR, APY, investment return, or irregular cash-flow yield.
If \(i_{eff}\) is an effective annual rate and there are \(m\) equal compounding periods, the equivalent periodic rate is:
Suppose the effective annual rate is 12.6825% and the desired period is one month:
Dividing 12.6825% by 12 would produce about 1.0569%, which is not the equivalent monthly compound rate.
| Period | Common nominal conversion | What to verify |
|---|---|---|
| Monthly | Annual nominal rate / 12 | Billing-cycle length, average daily balance, compounding, grace period |
| Quarterly | Annual nominal rate / 4 | Coupon or payment date versus compounding date |
| Semiannual | Annual nominal rate / 2 | Bond-market quotation and day-count convention |
| Daily, 365 basis | Annual nominal rate / 365 | Leap-year treatment, actual days, balance method |
| Daily, 360 basis | Annual nominal rate / 360 | Whether actual/360, 30/360, or another convention applies |
| Weekly | Annual nominal rate / stated periods | Whether the contract uses 52, actual days, or another basis |
The divisor is part of the financial convention, not a natural constant. A daily rate based on 360 and a daily rate based on 365 produce different accruals from the same annual quote.
Assume a line of credit states a 24% APR and the agreement defines the daily periodic rate as APR divided by 365. Ignore fees, grace periods, compounding, and rate changes for this simplified example.
The daily rate is:
The balance is GBP 3,000 for 10 days, falls to GBP 2,000 after a payment, and remains there for 20 days.
Applying the rate to GBP 3,000 for all 30 days would produce about GBP 59.18 and overstate the simplified accrual by GBP 13.15. The transaction date and balance path matter as much as the displayed annual rate.
A real credit agreement can use an average daily balance, separate transaction categories, a grace period, minimum charges, fees, and a statement-specific number of days. The actual disclosure and statement method control.
A periodic interest rate is not a payment amount. For an amortizing loan, the payment also depends on principal, term, number of payments, payment timing, and whether the rate changes.
For a level-payment loan with periodic rate \(i_p\), principal \(P\), and \(N\) end-of-period payments, the standard payment formula is:
That formula is not suitable without adjustment for irregular first periods, fees financed into the balance, interest-only stages, balloon payments, changing rates, or payments at the beginning of each period.
The phrase can refer to a contract rate, an accounting input, or a model conversion. Each use needs the correct source and convention.
This page provides general financial education, not legal, lending, deposit, accounting, tax, investment, or personalized financial advice. Product calculations depend on the current agreement and applicable disclosure rules.