How to Calculate Per Diem on an Auto Loan

To calculate per diem on an auto loan, multiply your current outstanding principal balance by your annual contract interest rate, then divide by the number of days specified by your lender's calculation method. With a 365-day basis, the formula is:

Daily interest = principal balance × (annual interest rate ÷ 100) ÷ 365

For example, if we owe $20,000 in principal at an 8% annual interest rate, our daily interest is $4.38, rounded to the nearest cent. If that balance and rate stay unchanged for 10 days, the estimated interest is $43.84. We calculate that total using the unrounded daily figure.

Understanding this number helps us check an interest charge, plan a refinance, or estimate how much interest could accrue before a payoff reaches the lender. Below, we walk through the calculation and explain which details can change the result.

Use the calculator on this page to estimate daily interest and interest over a chosen number of days. Enter the outstanding principal, annual contract interest rate, and day-count basis. Use a manual day count or calculate the calendar days between two dates.

The optional payoff section adds existing unpaid interest and known fees to the principal and the newly calculated interest. It is an estimate based on your inputs. Before sending a final payment, obtain an official payoff quote from your lender.

What Does Per Diem Mean on an Auto Loan?

In auto lending, per diem means the dollar amount of interest accruing per day. It is different from your daily interest rate: the rate is a percentage, while the per diem is a money amount.

Chase explains its daily simple-interest calculation as the outstanding principal multiplied by the annual interest rate divided by 365. That gives us a daily borrowing cost tied to the principal we still owe.

We can think of the two inputs separately. The contract rate describes how expensive each borrowed dollar is. The outstanding principal describes how many dollars are still borrowed. Together, they determine the daily interest amount.

Per Diem Interest vs. Your Monthly Payment

Per diem interest is one part of borrowing costs, while a monthly payment also repays principal. Suppose our loan accrues approximately $4.38 daily and our payment is $450. The $4.38 is not a daily installment, and multiplying $450 by the number of days would not help us calculate interest.

Instead, we use the daily interest amount to estimate the interest for a period. The monthly payment is a separate figure used to meet the repayment schedule. Keeping these numbers separate makes the statement easier to read.

Per Diem Interest vs. Your Payoff Amount

A payoff amount is the amount needed to settle the loan for the date specified in the quote. Chase tells auto borrowers to obtain a payoff quote and notes that the amount is valid through the date shown.

We should therefore treat the daily interest figure as a component of a payoff estimate. A lender's quote may already include interest through its good-through date. Adding that same period of interest again would overstate what we owe.

The Auto Loan Per Diem Formula

For a loan using daily simple interest, we can express the calculation as:

Per diem = P × r ÷ D

Where:

• P is the outstanding principal balance.
• r is the annual contract interest rate expressed as a decimal.
• D is the annual day-count denominator used for the calculation.

To estimate interest for a period when the principal and rate remain constant:

Period interest = P × r ÷ D × N

Here, N is the number of calendar days in that period. These equations are the arithmetic behind the calculator. They assume no intervening principal changes and no compounding of the calculated interest.

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Use the Contract Interest Rate, Not Automatically the APR

The CFPB distinguishes the interest rate from APR: APR reflects the interest rate plus certain borrowing fees. For the daily interest calculation, we need the annual rate the contract uses to accrue interest. If the APR differs, substituting it can distort the estimate.

For a hypothetical comparison, take a $20,000 principal balance, an 8% contract interest rate, and an 8.5% APR. Using 8% with a 365-day denominator gives $4.38 daily. Using 8.5% gives $4.66 daily. That difference comes entirely from changing the input; it is not proof that the lender charged extra daily interest.

Check the Day-Count Basis

Bank of America states that its auto loan calculation divides annual interest by 365, or 366 in a leap year. Chase's educational explanation uses 365. These examples show why we should check our own lender's method rather than assume that every loan uses the same denominator.

The calculator offers fixed 365, fixed 366, and fixed 360 denominators, plus an Actual/Actual option that splits date ranges by calendar year. Select 360 only if your contract specifically calls for that denominator with actual elapsed days. This tool does not implement 30/360 date-count rules.

How to Calculate Per Diem on an Auto Loan Step by Step

Step 1: Find the Current Principal Balance

Start with the amount labeled outstanding principal or principal balance. For this calculation, we want the remaining borrowed amount, rather than the original vehicle price, original loan amount, next payment due, or a payoff quote that already includes interest.

If the account screen displays only a total balance, check whether accrued interest or fees are included. When the label is unclear, ask the lender for the current principal separately. An accurate formula cannot correct an input that represents the wrong thing.

Step 2: Convert the Annual Percentage to a Decimal

Divide the annual percentage by 100. An 8% rate becomes 0.08, a 6.5% rate becomes 0.065, and an 11.25% rate becomes 0.1125.

For hand calculations, use the decimal. In our calculator, enter the percentage itself: type 8 for 8%. Entering 0.08 in the percentage field would mean 0.08%, producing a result 100 times too small.

Step 3: Multiply Principal by the Annual Rate

With $20,000 at 8%, we calculate:

$20,000 × 0.08 = $1,600

This is an annualized interest amount on an unchanged $20,000 balance. We should not interpret it as a prediction of actual interest over the next year, because the principal may decline as payments are applied.

Step 4: Divide by the Correct Denominator

Using a 365-day basis:

$1,600 ÷ 365 = $4.3835616438 per day

Our displayed per diem is $4.38. With a fixed 366 denominator, the same example gives $4.37 after rounding. The difference is small per day, but selecting the right denominator helps us compare the estimate with a statement.

Step 5: Multiply by the Number of Days

For 10 days on the unchanged balance:

$4.3835616438 × 10 = $43.8356164384

The rounded result is $43.84. If we multiply the already rounded $4.38 by 10, we get $43.80 instead. Our calculator retains precision internally and rounds the displayed amounts at the end. A lender's own posting and rounding rules can still produce a small difference.

Worked Example: $25,000 at 7.5%

Let's use another hypothetical loan to make the calculation easier to check independently.

First, we calculate $25,000 × 0.075 = $1,875. Then we divide by 365 to get $5.1369863014 daily. Finally, we multiply by 15 to get $77.0547945205.

The estimated per diem is $5.14, and the estimated 15-day interest is $77.05. Both displayed amounts come from the same unrounded calculation, which explains why multiplying $5.14 by 15 gives a slightly different result.

Daily Interest Examples at Different Balances and Rates

The following figures use a fixed 365-day denominator. The 10-day column assumes no payments or rate changes during those days. These are illustrative calculations, not current lending offers.

When we compare examples, we need to notice both inputs. A larger principal can generate more daily interest even at a lower rate. Conversely, a smaller balance at a higher rate may still have a lower dollar per diem.

How to Count Days for Auto Loan Interest

For a manual estimate, determine the period during which the balance and rate stayed unchanged. Bank of America's instructions use calendar days elapsed since the last payment.

Our date mode measures the calendar difference between the start and end dates: June 1 to June 11 is 10 days. Equal dates produce zero days. It treats the interval as start-inclusive and end-exclusive for splitting interest across calendar years.

That convention makes the tool predictable, but your lender decides the effective dates used on your account. Confirm whether interest is paid through a particular date and when a payment becomes effective. Use the manual-day option if the lender gives you a specific day count.

What Happens Across a Leap Year?

If a contract uses a fixed denominator, we keep that denominator even when the date range crosses a year boundary. If it uses Actual/Actual, each part of the interval uses the number of days in its own calendar year.

For example, December 30, 2027, to January 3, 2028, spans four days under our convention. On a $20,000 balance at 8%, an Actual/Actual estimate uses two days divided by 365 and two divided by 366:

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$1,600 × (2 ÷ 365 + 2 ÷ 366) = $17.51, rounded.

This is an illustration of the selected calculation method, not a claim that every lender changes its denominator on January 1. Check the contract before choosing this setting.

How to Estimate an Auto Loan Payoff

When we start from principal rather than an existing quote, a simplified estimate is:

Estimated payoff = principal + existing unpaid interest + new period interest + known fees

Suppose our example has $20,000 principal, $32.50 existing unpaid interest as of the start date, $43.84 newly estimated interest for 10 days, and $15 in known applicable fees. The estimated payoff is $20,091.34.

The optional calculator fields follow this structure. Existing interest must cover the period before the new interval; otherwise, we could count the same interest twice. Enter only fees known to apply to the payoff. The tool does not determine charges, refunds, credits, or adjustments for us.

Avoid Adding Interest Twice to a 10-Day Payoff Quote

If we already have a lender quote good through a future date, we should use that quote's instructions. Do not paste the quoted total into the principal field and add another 10 days of interest.

For example, a quote that already includes interest through June 11 should not receive a second June 1–11 interest addition. If the payment will arrive later, request an updated quote or ask the lender how to use any stated additional per diem. The calculator's estimate helps us understand the math; the quote controls the settlement amount.

Why Per Diem Changes After Payments

For the same rate and denominator, a lower principal produces a lower daily interest amount. The Federal Reserve's explanation of daily simple interest connects earlier principal reduction with less interest accruing over time.

In our 8% example, reducing principal from $20,000 to $19,000 changes per diem from approximately $4.38 to $4.16. The exact reduction is $1,000 × 0.08 ÷ 365, or about $0.22 daily.

We must use the amount actually applied to principal. A $500 payment does not automatically mean a $500 principal reduction. The CFPB explains that payments generally cover fees first, then interest, with the remainder reducing principal.

Split the Calculation When Principal Changes

Imagine $20,000 at 8% for 10 days, followed by $19,000 at 8% for another 10 days. We calculate each period separately:

• First interval: $20,000 × 0.08 ÷ 365 × 10 = $43.84, rounded.
• Second interval: $19,000 × 0.08 ÷ 365 × 10 = $41.64, rounded.
• Combined interest, rounded after adding the unrounded intervals: $85.48.

Using the original $20,000 for all 20 days would overestimate this example. Using the new $19,000 for the entire period would underestimate it. Our calculator handles one constant-principal interval at a time, so run it separately for each interval when payments change the balance.

Does Paying Late Increase Daily Interest?

Additional days before principal is reduced can increase interest costs. Chase's final-payment guidance explains that late payments can leave more principal outstanding than planned and may also involve late fees.

Using our hypothetical $20,000 balance at 8%, five extra days with no principal change add $21.92 in interest. That calculation does not include late fees and does not describe a lender's grace period. It simply isolates the interest from five additional days.

We should also distinguish interest timing from due-date rules. A payment being accepted within a fee grace period does not tell us, by itself, which days the contract includes in interest accrual. Ask the lender if the account's treatment is unclear.

When This Calculator Does Not Fit the Loan

The CFPB distinguishes simple-interest auto loans from precomputed-interest loans, where the interest is calculated at the outset. A daily simple-interest estimate should not be used as the payoff formula for a precomputed loan.

Our tool also does not calculate a full amortization schedule, compound interest, changing principal within one interval, or 30/360 date conventions. For a variable-rate loan, split the period whenever the rate changes. For a contract with a special interest method, ask for the lender's calculation rather than forcing it into a daily-simple-interest model.

Common Mistakes When Calculating Per Diem

Most avoidable errors involve inputs or timing. Before comparing the result with a lender statement, check these points:

• Original loan amount: replace it with the principal outstanding during the interval.
• APR substituted for interest rate: verify the contract rate used for accrual.
• Percentage entered as a decimal: type 8 in the calculator for an 8% rate.
• Rounded daily interest multiplied forward: retain precision until the final total.
• Payment within the interval: split the calculation at the effective principal change.
• Quote interest counted twice: identify the quote's good-through date before adding interest.
• Wrong date convention: compare your day count with the lender's effective dates.

If the estimate still differs, ask for the principal, annual rate, day count, denominator, and rounding method behind the charge. Those details give us a useful comparison without assuming that a small discrepancy proves an error.

Final Thoughts

Once we know the outstanding principal, contract interest rate, and day-count basis, calculating per diem on an auto loan is straightforward. Multiply principal by the annual rate as a decimal, divide by the appropriate denominator, and multiply by the days in an unchanged-balance interval.

Use the calculator to understand your daily borrowing cost and check scenarios. For an actual payoff, reconcile the estimate with the lender's dated quote and payment instructions so that existing interest and new interest are counted correctly.

Frequently Asked Questions

1. What is the per diem on a $20,000 auto loan at 8%?

With a fixed 365-day basis, the calculation is $20,000 × 0.08 ÷ 365, which equals approximately $4.38 daily. For 10 days on the unchanged balance, the estimated interest is $43.84, calculated before rounding.

2. Do we use APR or the interest rate for auto loan per diem?

Use the annual contract rate applied to interest accrual. APR can include certain fees, so it may differ from that rate. If the agreement shows only APR or the labels are unclear, ask the lender to identify the rate used in its daily calculation.

3. Is auto loan interest always divided by 365?

No single setting should be assumed for every loan. Check the contract or lender's instructions. The calculator supports fixed denominators and an Actual/Actual date mode, but selecting an option does not establish that it is the correct method for your account.

4. Can we calculate an exact payoff using per diem alone?

Per diem alone cannot establish the complete payoff. We also need the principal, existing unpaid interest, applicable charges or adjustments, and the lender's effective payoff date. Request an official quote before paying off the loan.

5. Why does daily interest fall as we repay an auto loan?

Under the daily-simple-interest model, the daily dollar amount is proportional to outstanding principal. If the annual rate and denominator stay unchanged, reducing principal reduces per diem. Recalculate after confirming how much of a payment actually reduced the principal.

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