Monthly Payment Calculator: Formula and Example

A monthly payment is the amount paid each month to repay a loan, including principal and interest. Enter the loan amount, annual percentage rate (APR), and term below to estimate the fixed monthly payment and total interest; the calculation assumes regular monthly payments and a fixed rate.

Formula

For a fixed-rate loan with equal monthly payments, the payment is calculated using the standard amortization formula:

Payment = P × r ÷ [1 − (1 + r)⁻ⁿ]

• P is the amount borrowed, in dollars.
• r is the monthly interest rate as a decimal: APR ÷ 12 ÷ 100.
• n is the total number of monthly payments: loan term in years × 12.

The calculator’s APR input is a percentage per year, so it uses r = APR ÷ 1200. Total interest is estimated as the rounded monthly payment multiplied by the number of payments, minus the original principal. Because the payment is rounded to cents, the calculated total is an estimate; a lender’s final payment schedule can include a slightly different final payment.

Worked Example

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

1. Convert the APR to a monthly decimal rate: 8 ÷ 1200 = 0.0066667.
2. Count the payments: 5 × 12 = 60 months.
3. Substitute into the formula: $20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰].
4. The unrounded monthly payment is about $405.527; rounded to the nearest cent, the payment is $405.53 per month.
5. Using that rounded payment, estimated total interest is ($405.53 × 60) − $20,000 = $4,331.80.

Assumptions

• The APR and payment amount remain fixed throughout the term.
• Payments are equal, made monthly, and begin one month after the loan is issued.
• Interest is treated as accruing monthly at APR ÷ 12.
• Fees, taxes, insurance, PMI, escrow, and any charges not entered in the calculator are excluded.

What a Monthly Payment Includes

For a standard installment loan, each scheduled payment covers interest accrued since the previous payment and pays down some principal. Early in the schedule, the interest portion is generally larger because interest is calculated on a larger outstanding balance. As principal falls, the interest portion tends to shrink and more of each level payment goes toward principal.

A loan payment is not always the same thing as the full monthly cost of borrowing or owning something. For example, a mortgage payment estimate may omit property-related costs and insurance, while an auto-loan payment estimate may omit registration, maintenance, and insurance. The calculator only models the loan principal and interest described by its inputs.

How to Use the Estimate

Use the amount actually financed as the loan amount, rather than the sticker price or purchase price if a down payment, trade-in, or other adjustment changes the amount borrowed. Enter the APR supplied in the loan disclosure or quote, not a monthly rate. Enter the repayment term in years; for a term quoted in months, divide the number of months by 12.

The result is most useful for understanding how the three inputs interact. With principal and APR unchanged, a longer term generally lowers the required monthly payment but increases the number of payments and can increase total interest. A higher APR generally increases both the payment and interest cost. These are mathematical effects under the formula’s assumptions, not a prediction of what terms a lender will offer.

• Check that the loan amount is the financed balance, not a total that includes excluded charges.
• Use the APR as a yearly percentage: enter 8 for 8%, not 0.08 or 8 divided by 12.
• Compare estimates using the same principal, APR definition, and term.
• Consider the displayed total interest alongside the monthly amount; a payment alone does not show the full repayment cost.

Limits and Common Misunderstandings

This formula applies to a fixed-rate loan repaid through equal monthly payments. It does not calculate a variable-rate payment, a loan with irregular payments, interest-only periods, a balloon payment, or a balance that changes because of extra payments. If the rate changes or the payment schedule differs, the actual payment path can differ from this estimate.

APR is entered as a yearly percentage, but the formula converts it to a monthly rate by dividing by 12. That is a simplifying convention for this calculator. Loan disclosures may calculate APR or interest using additional details, such as fees, payment timing, or a different accrual method. Do not assume the result includes fees merely because a quoted APR may reflect some borrowing costs.

Rounding also matters. The calculator rounds the monthly payment to cents and uses that rounded amount to estimate total interest. A real repayment schedule may adjust the last payment to clear the remaining balance, and the exact figures depend on the lender’s calculation and contract.

Frequently Asked Questions

How do I calculate a monthly loan payment?
Use the fixed-payment formula P × r ÷ [1 − (1 + r)⁻ⁿ], where P is the loan principal, r is the monthly rate as a decimal, and n is the number of monthly payments.

Does a monthly payment include interest?
For a standard amortizing loan, yes. Each payment includes interest and principal, although the proportion allocated to each changes over the repayment period.

Why is my lender’s payment different from this estimate?
The lender may use different payment timing or rounding, or include financed fees or other charges. Compare the calculator’s inputs and assumptions with the lender’s payment schedule and disclosure.

Does a longer loan term lower the monthly payment?
For the same principal and fixed APR, extending the term generally lowers the scheduled payment because repayment is spread across more months. It can also increase total interest because the balance remains outstanding longer.

Is this the full monthly cost of a mortgage or car loan?
No. This estimate covers modeled principal and interest only. Other expenses, such as insurance, taxes, escrow, or vehicle costs, are not included unless separately entered.

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