Every loan payment, savings credit and credit card statement uses a periodic interest rate — the rate for one day, one month or one quarter — even though the rate you are quoted is annual. Most of the time the conversion is simple division, but when compounding and payments run on different schedules it is not. This calculator gives the exact rate per period for any combination and shows how far simple division would be off.
How to use the periodic interest rate calculator
- Enter the nominal annual rate (APR).
- Choose how often interest is compounded.
- Choose the payment or crediting frequency you need a rate for.
- Optionally enter a balance to see the interest for one period.
- Read the periodic rate, the simple-division figure, the effective annual rate and the daily periodic rate, then compare all frequencies in the table.
Periodic rate formulas
When payments and compounding match (m = p):
When they differ:
r is the nominal annual rate, m the compounding periods per year and p the payment periods per year.
Worked examples
Matching schedules: 6% compounded monthly, paid monthly → i = 0.06 ÷ 12 = 0.5%. Interest on $1,000: $5.00.
Different schedules: 6% compounded semi-annually, paid monthly → i = (1.03)1/6 − 1 = 0.493862%. Dividing by 12 would overstate it at 0.5%.
Bi-weekly payments: 6% compounded monthly, paid every two weeks → i = (1.005)12/26 − 1 = 0.230459%, slightly below 6% ÷ 26 = 0.230769%.
True periodic rates for 6% compounded monthly
| Payments | True periodic rate | APR ÷ periods |
|---|---|---|
| Weekly | 0.115163% | 0.115385% |
| Bi-weekly | 0.230459% | 0.230769% |
| Monthly | 0.500000% | 0.500000% |
| Quarterly | 1.507513% | 1.500000% |
| Annually | 6.167781% | 6.000000% |
When payments are less frequent than compounding, interest compounds within each payment period, so the true rate is higher than simple division. When payments are more frequent, it is lower.
Where periodic rates matter
Credit cards
Card agreements list a daily periodic rate, usually APR ÷ 365. Interest is charged on the average daily balance for the billing cycle. At 22.9% APR the daily rate is about 0.0627%; with daily compounding, a month’s interest on $1,000 comes to about $19.26, or roughly 25.7% a year on an effective basis.
Mortgages and auto loans
US installment loans typically use APR ÷ 12 as the monthly rate. Canadian fixed-rate mortgages are quoted with semi-annual compounding, so the monthly rate must be converted — see the equivalent interest rate calculator.
Savings and investments
Accounts that compound daily but credit monthly, or funds that report quarterly returns, all rely on the same conversion. To grow a balance at a known periodic rate, use the periodic compound interest calculator.
Results are exact conversions. Lenders and banks may round periodic rates or use a 360-day year, so small differences from your statement are normal.
Frequently asked questions
What is a periodic interest rate?
It is the rate applied in each period — each day, month or quarter — rather than over a year. When interest compounds monthly, the periodic rate is the annual rate divided by 12; a 6% APR is 0.5% a month.
How do I calculate the periodic rate when payments and compounding differ?
Use i = (1 + r/m)^(m/p) − 1, where r is the nominal annual rate, m is compounding periods per year and p is payment periods per year. For 6% compounded semi-annually with monthly payments, i = 1.03^(1/6) − 1 = 0.493862% a month, not 0.5%.
What is a daily periodic rate on a credit card?
Most US card issuers divide the APR by 365 to get the daily periodic rate and apply it to your balance each day. A 22.9% APR has a daily periodic rate of about 0.0627%, which works out to about $19.26 of interest a month on a $1,000 balance if it compounds daily.
Why not just divide the APR by the number of payments?
Simple division is exact only when payments and compounding happen on the same schedule. Otherwise it slightly misstates the rate, which adds up over a long loan. The table on this page shows both figures side by side.