Loan Payoff Formula: Calculate Your Monthly Payment

The loan payoff formula calculates the level monthly payment needed to repay a fixed-rate loan over a set term, along with the total interest paid. Enter the original loan amount, annual percentage rate (APR), and term to see an estimated payment and interest total.

Formula

For a fixed-rate loan repaid with equal monthly payments, the payment is calculated as:

Payment = P × r ÷ [1 − (1 + r)⁻ⁿ]

• P is the starting loan principal, in dollars.
• r is the monthly interest rate as a decimal: annual APR ÷ 12 ÷ 100.
• n is the number of monthly payments: years × 12.

The calculator rounds the monthly payment to the nearest cent. It then estimates total interest as rounded monthly payment × number of payments − principal. Because the rate is entered as a percentage, the calculator uses apr / 1200 for r. For example, an 8% APR becomes a monthly rate of 8 ÷ 1200, or about 0.006667.

Worked Example

Using the calculator’s default inputs—$20,000 principal, 8% APR, and a five-year term:

1. Convert the APR to a monthly decimal rate: 8 ÷ 1200 = 0.0066667.
2. Convert the term to monthly payments: 5 × 12 = 60.
3. Substitute into the formula: $20,000 × 0.0066667 ÷ [1 − (1 + 0.0066667)⁻⁶⁰].
4. The unrounded payment is about $405.53; rounded to cents, the monthly payment is $405.53.
5. Calculate interest using the rounded payment: $405.53 × 60 − $20,000 = $4,331.80.

Assumptions

• The interest rate stays fixed for the full term.
• Payments are equal, made monthly, and treated as occurring at the end of each period.
• Interest is compounded monthly using APR ÷ 12. Actual contract calculations can use different conventions.
• Fees, taxes, insurance, mortgage insurance, escrow, and other charges are not included.

How the Payoff Formula Works

Each scheduled payment covers the interest accrued since the prior payment and reduces principal by whatever remains. Early in the schedule, the outstanding balance is larger, so more of each payment goes to interest. As the balance falls, the interest portion generally shrinks and more of the payment reduces principal. This changing allocation is called amortization.

The formula sets the payment so that, under its assumptions, the balance reaches zero after n payments. A longer term spreads repayment over more months and usually produces a smaller required monthly payment, but also gives interest more time to accrue. A shorter term generally means larger scheduled payments and fewer periods of interest. These are mathematical effects, not a recommendation about which term to choose.

The result is a scheduled-payment estimate, not a payoff quote for a specific date. A lender’s payoff amount can differ because interest may accrue daily, the payment date may not match the calculation period, or the account may include fees or other adjustments. Ask the lender or servicer for the exact amount and date when one is needed.

Using and Interpreting the Estimate

Enter the amount borrowed, the APR shown for the loan, and its term in years. Check that the APR and term match the figures in the lender’s disclosure. The payment result is the calculated regular monthly amount; total interest is the sum of those rounded payments minus the original principal.

Total interest is not the same as total paid. In this example, 60 payments of $405.53 equal $24,331.80 altogether. Subtracting the $20,000 borrowed leaves $4,331.80 in estimated interest. The total paid may be higher if the actual loan has charges excluded from this calculation.

APR can reflect certain borrowing costs in a lender’s stated disclosure, but this simple formula treats the entered APR as the periodic interest-rate basis. It does not separately model financed fees, payment-specific charges, or a changing rate. Use the loan documents’ stated payment and cost figures when they differ from this estimate.

Common Errors and Formula Limits

• Mixing annual and monthly rates: Do not enter 8 as the monthly rate. Enter 8 in the APR field; the calculator converts it to a monthly decimal.
• Using the wrong term unit: The term field is years, not months. A five-year term means 60 payments.
• Rounding too early: Keep the rate and formula at full precision, then round the payment to cents. This calculator uses that rounded payment for its interest total.
• Assuming every debt uses level payments: Variable-rate loans, interest-only periods, balloon payments, irregular schedules, and revolving credit balances do not necessarily follow this formula.
• Confusing a scheduled payment with early payoff: Extra payments can reduce principal and change later interest, but their effect depends on how the lender applies them and whether the schedule is recalculated.

The formula also presumes a positive APR and at least one monthly payment. It cannot reproduce a lender’s precise day-by-day accrual, contractual rounding, payment posting rules, or account-specific adjustments. Obtain the actual loan terms and figures from the lender rather than treating this estimate as a statement balance.

Frequently Asked Questions

What is the basic loan payoff formula?
For equal monthly payments, use P × r ÷ [1 − (1 + r)⁻ⁿ], where P is principal, r is the monthly rate as a decimal, and n is the number of payments.

How do I convert APR to a monthly rate?
For this calculation, divide the APR percentage by 1,200. An 8% APR becomes 8 ÷ 1,200 = 0.0066667 per month.

Does the monthly payment include all loan costs?
No. The estimate excludes charges such as fees, taxes, insurance, and escrow unless they are explicitly included in the entered loan amount or rate. Check the lender’s disclosure for the complete payment details.

Why can my lender’s payment or payoff quote differ?
The loan may use a different accrual convention, payment schedule, rate, fee treatment, or rounding method. A dated payoff quote can also include accrued interest or account adjustments not represented here.

Does paying extra change the formula’s result?
The displayed result assumes only the stated level monthly payment. Extra principal payments can affect the remaining balance and interest, but the calculator does not model their timing or how the servicer applies them.

This result is an estimate, and the lender’s disclosure gives the exact figures.

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in p | Loan amount | $ | 20000 | 1 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in yrs | Loan term | years | 5 | 0.0833 | 50
out pmt | Monthly payment | $ | p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2