Exact Monthly Loan Payment Calculator

This calculator estimates the exact monthly payment for a fixed-rate, fully amortizing loan using the loan amount, annual percentage rate (APR), and term. Enter those three figures to see the monthly payment and the total interest implied by making that rounded payment for every month of the term.

Formula

For a fixed rate and equal monthly payments, the payment is calculated with the standard amortizing-loan 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 ÷ 1,200. The APR is entered as a percentage per year, so an 8% APR gives r = 0.08 ÷ 12.
• n is the number of monthly payments: loan term in years × 12.

The calculator displays the payment to the nearest cent. Its total-interest estimate is the displayed monthly payment multiplied by the number of payments, minus the original principal: Total interest = monthly payment × n − P. Because that calculation uses the payment rounded to cents, the displayed total follows the same convention.

Worked Example

Using the calculator’s defaults—$20,000 borrowed, 8% APR, and a 5-year term:

1. Convert the APR to a monthly decimal rate: 8 ÷ 1,200 = 0.0066666667.
2. Find the number of payments: 5 × 12 = 60 months.
3. Substitute into the formula: $20,000 × 0.0066666667 ÷ [1 − (1.0066666667)⁻⁶⁰].
4. The unrounded result is approximately $405.527; rounded to cents, the monthly payment is $405.53.
5. Using the rounded payment, total scheduled payments are $405.53 × 60 = $24,331.80. Subtract $20,000 principal: estimated total interest is $4,331.80.

Assumptions

• The interest rate stays fixed for the full term.
• Payments are equal, made monthly, and the first payment is one month after the loan starts.
• Interest is treated as compounding monthly at APR ÷ 12.
• Fees, taxes, insurance, mortgage insurance, escrow, and other charges are not included.

What the Monthly Payment Includes

The result is the scheduled principal-and-interest payment under these assumptions. At the beginning of a typical amortizing loan, more of each payment goes toward interest because the outstanding balance is larger. As the balance falls, the interest portion generally shrinks and more of each fixed payment reduces principal. The loan is designed to reach a zero balance after the final scheduled payment, subject to the calculation’s assumptions and rounding.

A quoted monthly housing cost or vehicle cost may be higher than this loan payment. For example, a mortgage payment shown in a household budget can also include property-related charges or insurance, while this calculator models only principal and interest. Similarly, a lender may collect fees separately or include financed charges in the amount borrowed. To model a financed charge, include it in the loan amount only if that matches the figure and terms being evaluated.

How to Use and Read the Estimate

Enter the amount actually financed, not necessarily the advertised purchase price. Use the APR supplied for the specific loan as a percentage—for example, enter 8 for 8%, not 0.08. Enter the repayment term in years; a 30-month term can be entered as 2.5 years. The calculator accepts terms from 0.0833 to 50 years, corresponding approximately to one month through 600 months.

The first result is the monthly payment rounded to cents. The second is estimated interest over the full scheduled term, not the total amount paid. Add the original principal to total interest to obtain the calculator’s estimated total scheduled payments. If a payment amount is quoted without a clear indication of what it includes, check the lender’s loan disclosure rather than assuming it matches this principal-and-interest figure.

To see how term changes affect the arithmetic, compare otherwise identical entries. A longer term means more monthly payments; it can lower the calculated payment while increasing total interest, because the balance is outstanding for more months. A shorter term generally means fewer payments and a higher payment per month. These are formula outcomes, not a recommendation about which term to select.

Common Sources of Differences

• APR versus monthly rate: Enter annual APR as a percent. The formula converts it to a monthly decimal by dividing by 1,200; entering a monthly rate as though it were APR produces a different result.
• Amount borrowed versus purchase price: A down payment, trade-in, or other adjustment can make the financed principal differ from the item’s price.
• Fees and add-ons: The calculator has no separate input for origination charges or other costs. Whether a charge is paid separately or financed changes the actual cash flows.
• Rounding and payment dates: The tool rounds the regular payment to cents. A lender may calculate interest using specific dates, daily accrual, or other contract details, and the last payment may be adjusted to clear a small remaining balance.
• Changing rates or payment schedules: The formula assumes a fixed rate and monthly payments. It does not model variable rates, skipped payments, extra principal payments, or payment frequency other than monthly.

Frequently Asked Questions

How do I calculate an exact monthly loan payment?
Use the amortizing-payment formula with the principal, monthly rate, and number of monthly payments. This calculator performs that calculation and rounds the monthly amount to the nearest cent. A lender’s contract may use additional details that affect the actual schedule.

Does the monthly payment include interest?
Yes. The result combines principal repayment and interest. It does not include fees, taxes, insurance, or other charges unless those amounts are part of the principal you enter.

Why is my lender’s payment different?
The lender may use a different financed amount, rate, term, payment date, fee treatment, or interest-accrual method. Compare the calculator inputs with the loan disclosure and confirm whether the quoted payment includes anything beyond principal and interest.

Is APR the same as the monthly interest rate?
No. APR is entered as an annual percentage. For this estimate, the monthly rate is APR divided by 12 and then expressed as a decimal, which is why the formula divides the percentage figure by 1,200.

Why can a longer loan term reduce the payment but increase interest?
Spreading repayment across more months reduces the amount due each month under the formula, but interest continues to accrue while principal remains unpaid. The total-interest output reflects the rounded monthly payment across the full term.

Is this the exact amount I will owe each month?
It is exact for the calculator’s stated inputs and assumptions, not a guarantee of a lender’s bill. Contract terms, fees, timing, and rounding can change the actual amount. 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