Monthly Payment Formula: How Loan Payments Are Calculated

The monthly payment formula calculates the fixed payment that repays a loan over a set number of months, given its principal and annual percentage rate (APR). Enter the loan amount, APR, and term below to estimate the monthly payment and total interest; the calculation assumes equal monthly payments and a fixed rate.

Formula

For a fixed-rate loan with a positive interest rate, the monthly payment formula is:

M = P × r ÷ [1 − (1 + r)⁻ⁿ]

• M is the monthly payment, in dollars.
• P is the starting principal, or amount borrowed, in dollars.
• r is the monthly interest rate as a decimal. For an APR entered as a percentage, r = APR ÷ 1,200. For example, 8% APR gives 0.08 ÷ 12 = 0.0066667 per month.
• n is the number of monthly payments. For a term in years, n = years × 12.

The formula finds a level payment whose monthly interest portion and principal portion together reduce the balance to zero after n payments. The calculator rounds the payment to the nearest cent. It then estimates total interest as the rounded monthly payment multiplied by the number of payments, minus the original principal. Because the payment is rounded, the final payment in an actual loan may be adjusted slightly.

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: r = 8 ÷ 1,200 = 0.0066667.
2. Convert the term to payments: n = 5 × 12 = 60.
3. Substitute the values: M = 20,000 × 0.0066667 ÷ [1 − (1 + 0.0066667)⁻⁶⁰].
4. Evaluate and round to cents: M ≈ $405.53 per month.
5. Estimate total interest using the rounded payment: $405.53 × 60 − $20,000 = $4,331.80.

Thus, the calculator returns a monthly payment of $405.53 and estimated total interest of $4,331.80. The total of all scheduled payments is $24,331.80 under this rounded-payment estimate.

Assumptions

• The APR and payment amount remain fixed for the full term.
• Payments are made monthly, at the end of each payment period.
• Interest is compounded monthly using APR ÷ 12 as the periodic rate.
• The estimate excludes fees, taxes, insurance, PMI, and escrow because they are not inputs.

How the Formula Works

Each payment covers interest accrued during the month and pays down some principal. Early in a typical amortizing loan, the balance is relatively large, so more of the payment goes to interest. As the balance declines, the interest portion generally shrinks and the principal portion grows. The payment stays level in this formula because it is calculated to distribute repayment across the full term.

The formula comes from the present value of a sequence of equal payments. Each future payment is discounted by the monthly rate; together, their present values must equal the amount borrowed. Solving that relationship for the payment gives the expression above. This is why the payment depends on all three inputs: a larger principal raises it, a higher rate raises it, and a longer term generally lowers the monthly amount while extending the repayment period.

When to Use It and How to Read the Result

Use the formula to estimate the scheduled principal-and-interest payment when the loan has a fixed rate, regular monthly payments, and a known term. It can help explain how changing one input alters the arithmetic, but it does not determine whether a loan is suitable or whether an applicant qualifies. Get the actual rate, fees, payment schedule, and loan terms from the lender’s disclosure.

• Monthly payment is the estimated amount due each month for principal and interest only.
• Total interest is the estimated interest over all scheduled payments, using the rounded payment.
• Total paid is the payment multiplied by the number of months; it includes repayment of principal as well as interest.

A lower monthly payment does not automatically mean less interest overall. A longer term spreads repayment across more months, which can reduce each payment while increasing the time interest accrues. The calculator reports the payment and interest estimate for the entered term; it does not include optional extra payments or changes in the rate.

Common Errors and Limits

A frequent mistake is dividing an APR by 100 and using that annual decimal directly as the monthly rate. For monthly payments, convert the percentage to a decimal and divide by 12: APR ÷ 1,200. Another is entering the term in months when the field requests years, or treating the loan amount as the amount ultimately paid after fees or add-ons. Check each input’s unit before interpreting the result.

Rounding can also create a small difference between a calculator estimate and a lender’s final schedule. This calculator rounds the regular payment to cents and multiplies it by the full number of payments to estimate total interest. A lender may calculate with greater precision internally and adjust the last payment to clear the remaining balance. Fees or other financed amounts can also change the principal used in a real schedule.

This standard formula does not describe variable-rate loans, irregular payment dates, interest-only periods, balloon payments, skipped payments, or loans with fees included in the APR calculation in a way that changes the repayment schedule. It also does not calculate a full payment that includes taxes, insurance, or escrow. For a zero-interest loan, the payment is simply principal divided by the number of payments; the calculator requires a positive APR, so that case is outside its input range.

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 use M = P × r ÷ [1 − (1 + r)⁻ⁿ].

Why divide APR by 1,200?
Dividing a percentage APR by 100 converts it to a decimal, and dividing by 12 converts the annual rate to a monthly rate. Together, those steps mean dividing by 1,200.

Does the formula include taxes and insurance?
No. It estimates principal and interest. Taxes, insurance, PMI, escrow, and fees are excluded unless separately included in the loan amount or payment details.

Does a longer loan term reduce total interest?
Not necessarily. It generally reduces the scheduled monthly payment, but repayment takes longer, so the total interest can be higher. The result depends on the principal, rate, term, and actual payment schedule.

Why is my lender’s payment different?
The lender may use a different principal, rate, payment date, rounding method, or repayment structure, or include charges not represented here. Compare the calculator’s assumptions with the lender’s disclosed schedule.

The 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