Daily Periodic Rate on a Loan: Formula and Calculator

Calculate a loan’s daily periodic rate by dividing its annual percentage rate (APR) by the number of days used in the lender’s year convention. Enter the APR and days per year to get the daily rate as a percentage and decimal; this is a rate calculation, not a daily payment or a complete interest charge.

Formula

Daily periodic rate = annual percentage rate ÷ days in the year used by the loan’s terms. In symbols, d = A / D, where d is the daily periodic rate in percent per day, A is the APR in percent per year, and D is the number of days in the lender’s stated rate year. To express the rate as a decimal per day, divide d by 100: r = A / (100 × D). Use the percent result when you want to quote the rate as a percentage; use the decimal result in an interest calculation.

The calculator uses the entered day count rather than deciding which convention applies. A 365-day year and a 360-day year produce different daily rates from the same APR. Some agreements may specify a particular method, so check the loan disclosure or agreement instead of assuming a convention.

Worked Example

Using the calculator defaults: APR A = 8%, and D = 365 days.

1. Divide the APR by days: 8 ÷ 365 = 0.0219178082… percent per day.
2. Rounded to six decimal places, the daily periodic rate is 0.021918% per day.
3. Convert the percentage to a decimal by dividing by 100: 0.0219178082… ÷ 100 = 0.0002191781… per day.
4. Rounded to eight decimal places, the decimal daily rate is 0.00021918.

For a simple illustration, if a balance were $1,000 for one day and interest were calculated by multiplying the balance by this decimal rate, the unrounded interest would be about $0.2192. The actual amount charged may differ because the lender’s balance method, day-count convention, payment timing, rounding, and other contract terms matter.

Assumptions

• The APR is fixed for this calculation and entered as a percentage per year.
• The entered day count is the annual divisor stated in the loan terms; it is not automatically adjusted for leap years.
• The calculator only converts an annual rate to a daily rate. It does not model payment timing, a changing balance, compounding, fees, taxes, insurance, PMI, or escrow.

What You’ll Need

• The loan’s APR, shown as a percent per year in the lender’s disclosure or agreement.
• The day-count convention used to determine daily interest, such as 365 or 360 days, if stated in the loan terms.
• A calculator, spreadsheet, or the calculator above. Keep the rate in percent until dividing, then convert it to a decimal if calculating interest.

Step-by-Step

1. Find the APR. Use the annual percentage rate relevant to the loan calculation. Do not substitute a monthly interest rate, payment amount, or a rate quoted for another period. If the rate can change, use the rate applicable to the period you are examining; this calculator itself assumes the entered rate stays fixed.
2. Confirm the day-count convention. Check the agreement or ask the loan servicer whether the daily calculation uses 365 days, 360 days, or another stated convention. A calendar year can contain 365 or 366 days, but a contract may define the divisor differently. Do not select 360 merely because it is convenient.
3. Enter the APR as a percentage. For example, enter 8 for an APR of 8%, not 0.08. The input accepts APR values from 0.01% to 100% because the calculator is designed for a positive annual rate within that range.
4. Enter the day count. Use the divisor from the loan terms. The calculator accepts whole-number values from 1 through 366; use the actual convention specified for the calculation rather than treating that range as a recommendation.
5. Divide APR by the day count. The result is the daily periodic rate in percent per day. For example, with an 8% APR and 365 days, the calculation is 8 ÷ 365 = 0.0219178…% per day.
6. Convert to decimal for interest arithmetic. Divide the daily percentage by 100. In the example, 0.0219178…% becomes 0.000219178… as a decimal. To estimate one day’s simple interest on a balance, multiply the balance by this decimal rate, but only if that matches the contract’s calculation method.
7. Keep precision until the end. Avoid rounding the daily rate too early. The displayed results are rounded for readability; retain more digits in intermediate calculations and apply the lender’s stated rounding method when comparing with a statement.
8. Check what the result represents. A daily periodic rate is not the same as the amount of interest for a day. The amount also depends on the balance subject to interest and the way interest is accrued and posted.

Common Mistakes

• Mixing up percent and decimal: 8% is 0.08 as a decimal. If calculating with a percent rate directly, remember to divide by 100; otherwise the interest result will be 100 times too large.
• Using 365 without checking: A lender may use a different stated day-count convention. Using the wrong divisor can make the calculated daily rate disagree with the loan documents.
• Confusing APR with the daily rate: APR is annual. The daily periodic rate is the annual percentage divided by the applicable day count; it is not the APR divided by 12.
• Calling the result a daily charge: The rate alone is not a dollar amount. A dollar estimate also needs the applicable balance and a matching accrual method.
• Rounding too soon: Rounding each intermediate step can create small differences over time. Use full precision during arithmetic, then round where the lender’s terms require it.

Tips

• Write down both the percentage rate and decimal rate, clearly labelled. This helps prevent using 0.021918 instead of 0.00021918 in a balance-times-rate calculation.
• For a quick independent check, calculate the daily rate using a second method or spreadsheet and compare before rounding.
• If comparing a calculation with a statement, use the statement’s balance and dates, and verify whether payments or other transactions changed the balance during the period.
• Ask the lender or servicer to identify the day-count basis and rounding procedure if the documents are unclear. Do not infer the contract method from a small difference in a sample calculation.

Troubleshooting

The result does not match a statement: Confirm the APR for the relevant date, the day-count divisor, the balance used, and the number of days accrued. Check for payments, new advances, rate changes, or rounding during the period. The calculator only converts APR to a daily rate, so it cannot reproduce a full account ledger.

The result looks 100 times too high or low: Check whether you entered APR as 8 rather than 0.08. When calculating dollars, use the decimal daily rate, not the percentage figure.

You cannot find the divisor: Look for language about daily interest, day-count basis, or interest accrual in the loan disclosure or agreement. If it is not clear, contact the servicer and ask which divisor applies to your account. Do not assume the calendar-day count is the contract’s convention.

The APR changes: Recalculate using the rate that applies to each relevant period. A single daily rate cannot represent periods with different APRs.

Frequently Asked Questions

What is a daily periodic rate on a loan?
It is the annual rate converted to a daily rate using the day-count convention specified for the loan. It may be used in calculating interest, but the rate alone is not a dollar charge.

How do I calculate a daily periodic rate?
Divide the APR expressed as a percentage by the applicable number of days in the rate year. Divide that percentage result by 100 to get a decimal rate.

Should I divide APR by 360 or 365?
Use the divisor stated in the loan terms or confirmed by the servicer. The correct convention depends on the particular agreement and calculation.

Is the daily periodic rate the same as the daily interest amount?
No. The rate is a proportion; a dollar amount also depends on the balance and the lender’s accrual and rounding methods.

Does this calculator account for leap years?
No. It uses the day count you enter. Follow the loan’s stated convention, which may or may not use 366 days in a leap year.

Can I use the daily rate to find total loan interest?
Not by itself. Total interest depends on balances, payments, timing, rate changes, and the contract’s calculation method. This result is an estimate; the lender’s disclosure gives the exact figures.

Related

• 30 Year Loan Repayment Calculator: Monthly Payment & Interest
• Loan Calculator Monthly Breakdown: Payment and Interest
• Advanced Loan Payment Calculator: Payments and Interest

in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in days | Days in rate year | days | 365 | 1 | 366
out rate | Daily periodic rate | % | apr / days | 6
out dec | Daily rate as decimal | - | apr / (100 * days) | 8