Monthly Payment Schedule Calculator and Loan Formula

This calculator estimates the fixed monthly payment on an amortizing loan from its principal, annual percentage rate (APR), and term in years. Enter those three figures to see the monthly payment and the total interest implied by making that payment for the full term.

Formula

The calculator uses the standard fixed-payment amortization formula. It converts the annual APR to a monthly rate, calculates the payment that pays down the principal and interest over the stated number of months, rounds that payment to the nearest cent, and estimates total interest using the rounded payment.

Monthly payment: 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, calculated as APR ÷ 1,200 when APR is entered as a percentage.
• n is the number of monthly payments, calculated as loan term in years × 12.

Total interest: I = M × n − P. Here, M is the payment rounded to cents, so the total reflects the displayed payment multiplied by the number of scheduled months. Actual loan statements can differ slightly because of payment dates, lender calculations, and a final adjusted payment.

Worked Example

Using the calculator defaults: principal P = $20,000, APR = 8%, and term = 5 years.

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 into the payment formula: M = 20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰].
4. The monthly payment is approximately $405.53 after rounding to cents.
5. Calculate total interest using the rounded payment: $405.53 × 60 − $20,000 = $4,331.80.

Assumptions

• The interest rate remains fixed for the full term.
• Payments are equal monthly payments, made at the end of each monthly period.
• Interest compounds monthly at APR ÷ 12.
• The calculation excludes fees, taxes, insurance, PMI, escrow, and other charges because they are not inputs.

What a Monthly Payment Schedule Shows

A monthly payment schedule is a plan for the repeated payments due during a loan term. A payment on an amortizing loan generally covers interest accumulated since the previous payment and applies the remainder to the principal. Early in the schedule, the balance is larger, so more of a level payment typically goes to interest. As principal is repaid, the interest portion usually falls and the principal portion rises.

This calculator gives the scheduled payment amount and estimated total interest, not a month-by-month table. A full amortization schedule would list, for each period, the opening balance, payment, interest charge, principal repaid, and closing balance. The pattern depends on the loan terms and how the lender applies payments.

How to Use and Read the Estimate

Use the amount borrowed as the principal, rather than the total of all future payments. Enter the annual APR as a percentage: for example, enter 8 for 8%, not 0.08. Enter the term in years. The first result is the estimated monthly principal-and-interest payment; the second is total interest over the entered term using that rounded payment.

For example, a quote may include a monthly amount for principal and interest plus separate charges. This calculator estimates only the principal-and-interest component. To understand a quoted amount, check whether it includes fees, insurance, taxes, or escrow, and whether the rate and term match the calculator inputs. Ask the lender for the exact figures and payment schedule.

What Changes the Payment

• Principal: A larger amount borrowed raises the payment when the APR and term are unchanged.
• APR: A higher entered rate raises the payment and usually increases total interest.
• Term: Spreading repayment over more months generally lowers the scheduled payment but can increase the total interest paid.
• Payment structure: The formula assumes equal payments and a fixed rate. Variable rates, interest-only periods, balloon payments, or irregular payment timing do not follow this result throughout the loan.

These are mathematical effects under the stated assumptions, not a recommendation about which terms to choose. Use the specific principal, rate, and term in a lender’s written disclosure when checking a real offer.

Limits and Common Mistakes

The formula is for a fully amortizing loan with a positive fixed APR and equal monthly payments. It does not determine a lender’s APR, account for a fee-financed balance, calculate a changing rate, or model missed or extra payments. If a lender uses a different day-count method or applies payments on different dates, its schedule may not match this estimate exactly.

• Do not confuse APR with the monthly rate. The calculator divides the entered annual percentage by 1,200 to get a monthly decimal rate.
• Do not treat total interest as the total amount repaid. The estimated total of payments is the rounded monthly payment multiplied by the number of months; principal is part of that amount.
• Rounding each payment to cents can cause a small difference from calculations that retain extra decimal places. A lender may adjust the final payment to clear the remaining balance.
• Check whether the quoted loan amount includes financed charges. Any amount added to principal changes the calculation.

Frequently Asked Questions

What does a monthly payment usually include?
The calculator estimates principal and interest only. Depending on the loan and the way a bill is presented, other charges may be listed separately or added to a payment; check the lender’s breakdown.

Does the payment stay the same every month?
This estimate assumes a fixed APR and level monthly payments. A variable rate, payment change, extra payment, or lender adjustment can make the actual amount or schedule different.

Why is the interest share larger at the beginning?
Interest is calculated on the outstanding balance. Because the balance is largest at the start, the interest portion of an equal payment is generally larger then; as principal falls, less interest accrues per period.

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 decimal rate by dividing by 1,200; actual APR disclosures and fees may involve details this calculator does not model.

Why might a lender’s payment differ?
The loan may have different inputs, financed fees, a different payment date convention, or charges outside principal and interest. Compare the loan amount, APR, term, and included charges, then use the lender’s disclosure for exact figures.

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