Daily interest formula
How to Calculate Daily Interest
Daily interest starts with the annual interest rate stated in the loan, note, payoff statement, or other governing document. Convert the percentage to a decimal, divide it by the day-count basis, and then multiply by the principal or payoff balance.
- P
- Principal or payoff balance
- r
- Annual rate written as a decimal
- d
- 360, 365, 366, or the basis required by the agreement
- n
- Number of days in the interest period
For example, a 7.5% annual rate is written as 0.075 in the formula. Using a 365-day basis, the daily periodic rate is 0.075 ÷ 365 = 0.00020548, which is about 0.020548% per day.
For 45 days, $5.136986 × 45 = approximately $231.16 in simple interest. The calculator above performs the same steps and also compares the result with 360- and 366-day bases.
Per diem interest calculator
What is per diem interest?
Per diem means “per day.” Per-diem interest is the dollar amount of interest that accrues for one day on a principal or payoff balance. The calculator above shows that dollar amount separately from the daily percentage rate so you can use it for payoff timing, mortgage closing interest, private notes, or any simple-interest calculation measured in exact days.
When exact dates matter, enter a start date and end date rather than manually counting days. You can also select whether the first date, last date, both dates, or neither date is included.
Daily rate and daily interest are not the same thing
Two numbers are often described as “daily interest,” but they answer different questions. The daily periodic rate is a percentage. The daily interest amount, also called per-diem interest, is a dollar amount.
| Measure | What it means | 7.5% annual rate example |
|---|---|---|
| Annual interest rate | The stated yearly rate | 7.5% |
| Daily periodic rate | Annual rate divided by the day-count basis | 0.020548% using 365 |
| Per-diem interest | Dollar interest charged for one day on the current balance | $5.14 on $25,000 |
| 45-day simple interest | Per-diem amount multiplied by 45 days | $231.16 |
This distinction matters when a payoff statement lists a “per diem.” A per-diem figure is normally a dollar amount to add for each additional day, not the percentage rate itself.
Actual/360 vs. Actual/365 vs. Actual/366
The denominator used to convert an annual rate into a daily rate can materially change the result. A smaller denominator creates a larger daily rate when the annual rate and balance are unchanged.
| Basis | Daily rate at 7.5% | Daily interest on $25,000 | Interest for 45 days |
|---|---|---|---|
| Actual/360 | 0.020833% | $5.21 | $234.38 |
| Actual/365 | 0.020548% | $5.14 | $231.16 |
| Actual/366 | 0.020492% | $5.12 | $230.53 |
Actual/360 is a common financial convention in which the annual rate is divided by 360 while the number of elapsed days may still be based on actual calendar days. Actual/365 divides by 365. A 366-day denominator may be used in some leap-year calculations or agreements.
Do not choose a basis simply because the calendar contains 365 or 366 days. The correct method is determined by the contract, lender calculation, statute, court order, or other rule that governs the interest.
How to calculate interest for any number of days
Once the per-diem amount is known, estimating simple interest for a period is straightforward:
Suppose the payoff balance is $80,000, the annual rate is 6%, the agreement uses Actual/365, and 17 days of interest are required:
- Convert 6% to 0.06.
- Calculate the daily rate: 0.06 ÷ 365 = 0.000164384.
- Calculate the per diem: $80,000 × 0.000164384 = about $13.15.
- Multiply by 17 days: about $223.56.
The final amount can differ if the governing document specifies a different day-count method, a particular rounding rule, compounding, payments during the period, or a different rule for counting the first and last day.
Can you calculate daily interest from APR?
If “APR” is being used informally to mean the stated annual interest rate, the daily-rate math is the same: convert the annual percentage to a decimal and divide by the required day-count basis.
However, a formally disclosed annual percentage rate (APR) can include certain fees or other finance-charge effects and may not be the same rate used to accrue interest on the unpaid principal. For a loan payoff or contractual calculation, use the interest rate and method required by the note, lender, or governing document rather than assuming the disclosed APR is the accrual rate.
How to convert a daily rate back to an annual or monthly rate
For a simple nominal-rate conversion, multiply the daily periodic rate by the same denominator that was used to create it. A daily rate of 0.020548% on a 365-day basis corresponds to approximately 7.5% per year.
A rough nominal monthly rate can be found by dividing the annual rate by 12. For a 7.5% annual rate, that is 0.625% per month. But a monthly rate is not interchangeable with a daily accrual rate because months contain different numbers of days.
If interest actually compounds every day, the effective annual return is a different calculation: (1 + daily rate)365 − 1. For example, 7.5% nominal interest compounded daily produces an effective annual rate of about 7.79%. The calculator above does not compound daily; it calculates simple daily interest.
Where daily and per-diem interest are commonly used
Daily interest calculations are useful whenever interest must be measured between exact dates rather than only at regular monthly payment intervals. Common examples include:
- Estimating a loan payoff between scheduled payment dates
- Adding per-diem interest when a closing or payoff date changes
- Private loans and seller-financed notes with irregular payment dates
- Reviewing simple-interest loan accruals
- Checking the effect of a late or early payment when the agreement accrues interest daily
- Estimating judgment or legal interest when the applicable rule uses a daily simple-interest method
These uses can have different legal and contractual rules. The calculator is a mathematical tool; it does not determine which rate, basis, date-count rule, or compounding method legally applies.
Common mistakes when calculating daily interest
- Using 7.5 instead of 0.075 in a manual formula. Percentages must be converted to decimals before multiplying.
- Assuming every loan uses 365. Many agreements specify 360, 365, 366, 30/360, Actual/Actual, or another convention.
- Confusing APR with the contractual interest rate. A disclosed APR can reflect more than the rate applied to principal.
- Rounding too early. Rounding the per-diem amount to cents before multiplying by many days can produce a slightly different result than rounding only the final total.
- Ignoring payments or balance changes. If the principal changes during the period, interest may need to be calculated separately for each balance segment.
- Assuming simple interest when the agreement compounds. Compounding requires a different formula.
Use the Right Daily Interest Calculator for the Job
If the exact start and end dates matter, use the Interest Between Dates Calculator to control which dates are counted. If you are extending a known balance through a future payoff date, use the Payoff Per Diem Calculator. For mortgage closing interest, use the Mortgage Per Diem & Prepaid Interest Calculator.