Calculate Loan Payments With This Formula and Calculator

This loan payment calculator estimates the fixed monthly payment and total interest for a fully amortizing loan. Enter the amount borrowed, annual interest rate (APR), and term in years; the results show the monthly payment and interest paid over the scheduled term.

Formula

For equal monthly payments on a fixed-rate, fully amortizing loan, calculate the payment as:

Monthly payment = round[P × r ÷ (1 − (1 + r)⁻ⁿ), 2]

• P is the starting loan principal, in dollars.
• r is the monthly interest rate as a decimal: APR ÷ 12 ÷ 100. With an 8% APR, for example, r = 0.08 ÷ 12.
• n is the number of monthly payments: years × 12.
• round(…, 2) rounds the scheduled payment to cents.

Total interest is estimated as monthly payment × n − P. Because the calculator uses the payment rounded to cents, this total reflects the displayed payment multiplied by the scheduled number of months. A lender’s final schedule can differ slightly if it handles the last payment or rounding differently.

Worked Example

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

1. Convert the APR to a monthly decimal rate: 8 ÷ 1200 = 0.0066667.
2. Convert the term to payments: 5 × 12 = 60 months.
3. Substitute into the payment formula: $20,000 × 0.0066667 ÷ [1 − (1 + 0.0066667)⁻⁶⁰].
4. The unrounded result is about $405.528; rounded to cents, the monthly payment is $405.53.
5. Total of scheduled payments: $405.53 × 60 = $24,331.80. Subtract principal: $24,331.80 − $20,000 = $4,331.80 total interest.

Assumptions

• The interest rate stays fixed throughout the stated term.
• Payments are equal, made monthly, and treated as occurring at the end of each monthly period.
• Interest accrues monthly using APR divided by 12, as this standard formula assumes.
• The estimate excludes fees, taxes, insurance, PMI, and escrow; these are not calculator inputs.

When to Use a Loan Payment Calculator

Use this calculation to understand the principal-and-interest payment implied by a stated amount, APR, and repayment period. It can help you examine how changing one input changes the arithmetic. For example, keeping the amount and APR fixed while extending the term generally lowers each scheduled payment but increases the number of payments over which interest is charged. The calculator does not determine whether a loan is suitable or whether a borrower will qualify.

Enter the lender’s quoted loan amount, APR, and term when you have them. If you are only exploring scenarios, treat the rate and amount as assumptions rather than quotes. Obtain the actual figures and payment schedule from the lender; rates, charges, and loan terms are specific to an offer and are not supplied by this calculator.

How to Read the Results

The monthly payment is the calculated amount applied each month under the formula’s assumptions. In a standard amortizing schedule, each payment covers interest accrued for that period and reduces some principal. Early payments generally allocate a larger share to interest than later ones because the outstanding balance starts higher. The total-interest figure is the estimated interest over all scheduled payments, not an additional monthly charge.

The payment shown is not necessarily the complete amount due on a real loan. A bill may include other amounts, and some loans use variable rates, irregular payment dates, interest-only periods, or a final balloon payment. Those arrangements are not represented by this fixed-payment calculation.

Common Mistakes and Limits

• Entering APR as a decimal: Enter 8 for 8%, not 0.08. The formula converts the percentage to a monthly decimal rate.
• Confusing years and months: The term field is in years. A five-year term is converted to 60 monthly payments.
• Using an incomplete borrowing amount: Enter the principal being repaid. If charges are added to the loan balance, the lender’s financed amount may differ from the amount received.
• Assuming APR captures every bill item: The calculator uses APR as its rate input, but it does not separately model fees, insurance, taxes, or other charges.
• Expecting a precise payoff quote: Actual interest can depend on payment dates, daily accrual, rounding, extra payments, and contract terms. This estimate does not replace a lender’s amortization schedule or payoff figure.

The formula also assumes a positive APR and a regular monthly schedule. It is not designed to calculate an adjustable-rate payment, a revolving balance, or a loan with changing payment amounts. If you make extra payments, the balance and total interest may change, but this calculator does not account for them.

Frequently Asked Questions

How do I calculate a monthly loan payment?
Convert APR to a monthly decimal by dividing it by 1,200, convert the term to months, then apply the fixed-payment formula shown above. Round the resulting payment to cents.

Does the monthly payment include the whole loan bill?
No. This result estimates scheduled principal and interest only. Fees, taxes, insurance, PMI, and escrow are not included.

Why does a longer loan term usually reduce the payment?
The principal is spread across more monthly payments. The schedule also runs for longer, so the total interest can be higher even when the monthly payment is lower.

Why does my lender’s payment differ from this estimate?
The lender may use different APR or principal figures, payment dates, rounding conventions, fees, or a different loan structure. Compare the inputs and ask for the lender’s payment schedule for the exact calculation.

Can this calculator handle a variable interest rate or extra payments?
No. It assumes a fixed rate and equal scheduled payments. A changing rate or extra principal payments requires a period-by-period calculation using the actual loan terms.

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 | $ | round(p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)), 2) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2