An interest rate factor is your annual interest rate expressed as a daily decimal: divide the APR by the number of days in the year, and the result is the share of each dollar of principal that accrues as interest in a single day. Lenders use it to calculate daily interest charges, per diem amounts on payoff quotes, and the interest portion of every scheduled payment. Once you know the factor, you can check almost any interest figure a lender hands you.
How to Calculate the Factor
Two steps. Convert the APR from a percentage to a decimal by dividing by 100, then divide that decimal by the days in the year your lender uses. A 7.25% rate becomes 0.0725, and 0.0725 ÷ 365 = 0.00019863. That decimal is the daily factor.
Lenders carry the result out to seven, eight, or ten places. Rounding early looks harmless on one day of interest and compounds into real dollars over the life of a loan, so keep the full decimal when you check their math. Federal law requires lenders to disclose the APR, which gives you the starting number for the calculation.1eCFR. 12 CFR Part 226 – Truth in Lending (Regulation Z)
The Denominator Matters: 360, 365, or 366
Not every lender divides by 365, and the choice quietly changes what you pay.
- Actual/365 divides the annual rate by 365 regardless of leap years. It’s the most common convention for residential mortgages and personal consumer loans.
- Actual/360 divides by 360 but counts the actual days in each month. A smaller denominator produces a larger daily factor. On a 6% loan, Actual/360 gives 0.00016667 against 0.00016438 under Actual/365, and across a full 365-day year the effective rate works out closer to 6.08%. Commercial real estate loans and business lines of credit commonly use this method.
- Actual/Actual uses 365 in ordinary years and 366 during leap years. It’s the most precise and is standard for U.S. Treasury securities and some adjustable-rate products.
Actual/360 has survived legal challenges on the condition that the lender discloses the calculation method. Two offers with the same stated APR are not actually the same loan if one uses a 360-day year and the other uses 365. The day count convention is usually set out in the promissory note.
Turning the Factor Into a Dollar Amount
Multiply the daily factor by your current principal balance. The product is the dollars of interest accruing that day.
A $250,000 mortgage with a daily factor of 0.0001849 accrues $46.23 in interest per day (250,000 × 0.0001849). That amount is added to what you owe every day the balance remains unpaid. Pay down principal and tomorrow’s charge drops, because lenders apply the factor to whatever the balance happens to be that day. Make a large principal payment on the 1st rather than the 15th and you avoid 14 days of interest at the higher balance, which on a $250,000 balance comes out to roughly $647.
Simple Interest vs. Daily Compounding
The factor behaves differently depending on how the loan handles yesterday’s interest.
Under simple interest, the daily factor applies to the principal balance only. Most mortgages and auto loans work this way, and the daily interest charge drops only when a payment reduces principal.
Credit cards generally compound daily. Interest calculated today is added to the balance, and tomorrow’s interest is calculated on that slightly larger number.2Consumer Financial Protection Bureau. What Is a Daily Periodic Rate on a Credit Card? Issuers call the daily factor the daily periodic rate, and it appears on your monthly statement. A card at 18% APR has a daily periodic rate of 0.18 ÷ 365 = 0.000493, so a $5,000 average daily balance costs roughly $2.47 per day. Federal law requires the billing statement to show both the periodic rate and the corresponding APR.3Office of the Law Revision Counsel. 15 USC 1637 – Open End Consumer Credit Plans
The gap between simple and compounded interest is small over a few weeks and widens the longer a balance sits. A $5,000 credit card balance at 22% APR compounded daily runs about $1,162 in interest over a year, against roughly $1,100 under simple interest.
Many card issuers calculate the monthly interest charge from an average daily balance: they total the day-end balances across the billing cycle, divide by the number of days, and apply the daily periodic rate to that average.4Consumer Financial Protection Bureau. How Does My Credit Card Company Calculate the Amount of Interest I Owe?
Using the Factor to Check a Payoff Quote
Payoff statements are where the factor earns its keep. When you request a payoff on a mortgage or auto loan, the lender gives a total owed through a specific date plus a per diem amount for each additional day. That per diem is just the daily factor applied to the remaining balance.
If a payoff letter shows $187,432.16 good through June 15 with a per diem of $34.52, closing on June 18 adds $103.56 (3 × $34.52). Federal law requires mortgage servicers to send an accurate payoff balance within seven business days of a written request.5Office of the Law Revision Counsel. 15 USC 1639g – Requests for Payoff Amounts of Home Loan Miss the good-through date without accounting for additional per diem, and the loan may not be fully satisfied. The leftover balance keeps accruing and can trigger late fees or show as delinquent.
Run the number yourself: daily factor times current balance should equal the per diem on the letter. If it doesn’t, the usual explanation is the day count convention. Ask whether the lender is using a 360-day or 365-day year.
When the Factor Shows Your Payment Isn’t Keeping Up
The same math exposes a problem that quietly wrecks household budgets: a monthly payment smaller than the interest accruing over that month. A $10,000 credit card balance at 24% APR generates roughly $200 in monthly interest. A $250 minimum payment reduces principal by only $50, and payoff stretches for decades.
In worse cases the balance grows while payments are made on time. Federal law defines this as negative amortization, where periodic payments result in an increase in the principal balance.6Legal Information Institute (LII). 15 USC 1639c – Minimum Standards for Residential Mortgage Loans – Definition of Negative Amortization Multiply the daily factor by the balance, then by the days in the billing cycle, and compare the result to your scheduled payment. The difference tells you how much of each payment is actually reducing what you owe.
Variable Rates
If your loan carries a variable or adjustable rate, the factor isn’t fixed. Each time the underlying index changes, the lender recalculates the rate and the factor along with it. If a new rate comes in at 7.0%, the daily factor becomes 0.070 ÷ 365 = 0.00019178. Comparing that to the figure on your adjustment notice is the quickest way to confirm the lender applied the change correctly.