Calculate a Monthly Loan Payment: Formula and Example

Calculate a fixed monthly loan payment by entering the amount borrowed, annual interest rate (APR), and loan term in years. This calculator returns the monthly principal-and-interest payment and estimated total interest, using a fixed rate and payments rounded to the nearest cent.

Formula

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

M = P × r ÷ [1 − (1 + r)⁻ⁿ]

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

The calculator’s APR input is a percentage per year, so it converts 8% to a monthly decimal rate of 8 ÷ 1,200. Its total-interest estimate is the rounded monthly payment multiplied by the number of payments, minus the original principal. Because the payment is rounded to cents, that estimate may differ slightly from an unrounded mathematical total or a lender’s final amount.

Worked Example

Using the calculator’s default inputs—$20,000 principal, 8% APR, and five years—the calculation has 60 monthly payments and a monthly rate of 8 ÷ 1,200 = 0.0066667.

1. Calculate the payment factor: 1 − (1 + 0.0066667)⁻⁶⁰ ≈ 0.32895.
2. Calculate the numerator: $20,000 × 0.0066667 ≈ $133.33.
3. Divide: $133.33 ÷ 0.32895 ≈ $405.53 per month, rounded to cents.
4. Estimate total interest using the displayed payment: $405.53 × 60 − $20,000 = $4,331.80.

So, under these assumptions, the estimated payment is $405.53 per month and estimated total interest is $4,331.80.

Assumptions

• The interest rate stays fixed for the full term.
• Payments are equal, made monthly, and applied at the end of each monthly period.
• Interest accrues monthly at APR divided by 12; the APR is treated as a nominal annual rate.
• The estimate excludes fees, taxes, insurance, PMI, escrow, and any charges not entered into the calculator.

When to Use the Estimate

This calculation is useful for understanding the scheduled principal-and-interest payment on a conventional fixed-rate installment loan. It can help you see how the amount borrowed, rate, and time period affect the payment mathematically. It does not determine whether a loan is suitable, what a lender will offer, or what payment fits a personal budget.

Use the amount that would actually be financed as the principal. If fees are added to the loan balance, the financed amount may be larger than the cash price or amount received. Enter the rate and term stated in the lender’s quote rather than assuming values from an example. For a term stated in months, divide the number of months by 12 to enter years; for instance, 48 months is four years.

Read the payment as the recurring amount for principal and interest only. A housing payment may also include taxes, insurance, mortgage insurance, or escrow; a vehicle payment can be affected by a deposit, trade-in, or final balloon payment. Those items are not included unless represented in the inputs, so the calculator result is not necessarily the full amount due each month.

What Changes the Monthly Payment?

• Principal: Borrowing more increases the payment when the rate and term stay the same.
• APR: A higher entered rate raises the payment and generally increases the total interest under this fixed-payment model.
• Term: Spreading repayment over more months usually lowers each scheduled payment, while increasing the number of months interest can accrue.
• Payment structure: A variable rate, interest-only period, deferred payments, balloon payment, or irregular payment schedule does not match this formula.

These are mathematical effects, not recommendations. To compare quoted loan estimates, use each quote’s own principal, APR, term, and payment structure, and account separately for any items the calculator leaves out.

Common Calculation Problems

A frequent mistake is entering an annual percentage as though it were a monthly decimal. For this calculator, 8% APR becomes 0.0066667 per month—not 8, 0.08, or 0.0067 as a percent input. The calculator performs this conversion automatically when APR is entered as 8.

Another common misunderstanding is that the payment is all interest or that the same amount of interest is charged every month. On an amortizing loan, each payment covers interest accrued on the remaining balance and reduces principal. Early payments generally contain a larger interest share; as the balance declines, more of a level payment goes toward principal. The formula assumes the scheduled payment is made on time and does not model extra payments or late charges.

Finally, the displayed payment is rounded to cents before total interest is calculated. A lender may use its own accrual dates, rounding methods, payment allocation, and contract terms. Small differences in a quote do not necessarily mean the formula is wrong.

Limits and Other Loan Types

This formula applies to a fully amortizing loan with a fixed rate, equal monthly payments, and no unusual payment features. It is not an exact model for a variable-rate loan, a loan with a changing payment, or a balance with fees or charges folded into the repayment schedule. To estimate an adjustable-rate loan, a single APR can only represent one assumed rate for the entire term; future rate changes are not predicted here.

For a more complete monthly housing-cost estimate, separately identify any taxes, insurance, mortgage insurance, or escrow amounts in the applicable disclosures. For a loan with a final balloon payment, the regular payment alone will not show the full amount due at the end. The lender’s repayment schedule and written disclosures contain the contract-specific figures.

Frequently Asked Questions

How do I calculate a monthly loan payment by hand?
Convert APR to a monthly decimal by dividing by 1,200, convert the term to months, then use M = P × r ÷ [1 − (1 + r)⁻ⁿ]. Round the result to cents for a payment estimate.

Does a monthly loan payment include interest?
The payment from this calculator includes both principal repayment and interest. It excludes separate costs such as fees, taxes, insurance, and escrow.

Why does a longer loan term lower the monthly payment?
A longer term divides repayment across more monthly payments. Although each scheduled payment may be lower, interest can accrue over more months, so the estimated total interest may be higher.

Is APR the same as the monthly interest rate?
No. APR is entered as an annual percentage here. The formula converts it to a monthly rate by dividing by 12 and then by 100. The calculator does not separately model fees that may be reflected in a disclosed APR.

Why is my lender’s payment different?
The lender may use different financed amounts, payment dates, fees, accrual conventions, rounding, or loan features. Compare the calculator’s assumptions with the lender’s written payment schedule.

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

Related

• Loan Calculator With Down Payment: Payment on What You Borrow
• Loan Payment Calculator: Monthly Payment, Total Interest and Cost
• Loan Calculator Based on Payment Amount: How Long to Pay It Off

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