Amortization Calculator: Find Your Monthly Payment

Yes. An amortization calculator can estimate a fixed-payment loan’s monthly principal-and-interest payment from the amount borrowed, annual interest rate, and loan term. Enter those three figures to see the payment and the total interest implied by the calculator’s assumptions.

Formula

The calculator uses the standard level-payment amortization formula. It first finds a payment that covers interest accruing each month and repays the principal over the stated number of months:

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

• P is the original loan principal, in dollars.
• r is the monthly interest rate as a decimal: annual APR ÷ 1,200. For an 8% APR, r = 8 ÷ 1,200.
• n is the number of monthly payments: loan term in years × 12.
• Payment is the monthly principal-and-interest amount, rounded to the nearest cent.

Total interest is calculated as monthly payment × number of payments − principal. Because the payment is rounded to cents first, the total is based on that rounded payment. A real lender’s final payment can differ slightly if its schedule adjusts the last installment or uses different rounding conventions.

Worked Example

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

1. Convert the annual APR to a monthly decimal rate: 8 ÷ 1,200 = 0.0066667.
2. Find the number of payments: 5 × 12 = 60.
3. Substitute into the formula: $20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰].
4. The monthly payment is approximately $405.53 after rounding to cents.
5. Total interest using the rounded payment is $405.53 × 60 − $20,000 = $4,331.80.

The payment is not simply the original balance divided by 60. Each month, part of the payment covers interest on the remaining balance; the rest reduces principal. Early in the schedule, the interest portion is larger because the balance is higher. As principal falls, the interest portion generally shrinks and more of each level payment goes toward principal.

Assumptions

• The interest rate is fixed for the full term.
• Payments are equal monthly installments, made at the end of each monthly period.
• Interest compounds monthly using the stated APR divided by 12.
• The estimate excludes fees, taxes, insurance, PMI, escrow, and other charges because they are not inputs to this calculator.

What the Payment Includes—and Leaves Out

The displayed monthly payment represents principal and interest only. A mortgage bill, for example, may also collect property-related costs or insurance, while a personal or auto loan may have fees or other charges handled separately. Those amounts are not part of this formula, so the calculator’s payment should not be read as a complete monthly bill.

APR is entered as a yearly percentage, not as a monthly percentage. The formula converts it to a monthly rate by dividing by 1,200. If a lender provides a payment quote, use the rate and term that apply to the specific loan and check whether the quoted amount includes any additional items. Obtain the actual figures and fee details from the lender rather than treating the example defaults as market rates.

How to Read and Use the Result

Use the result as a mathematical estimate when you want to understand how principal, rate, and term affect a level-payment loan. It can also help you inspect a proposed schedule: compare the calculated principal-and-interest amount with the payment information provided for the same balance, APR, term, and payment frequency. A mismatch can arise from different inputs, fees, payment timing, rate conventions, rounding, or a variable rate.

• Enter the amount financed, rather than a purchase price that includes a down payment not borrowed.
• Use the annual APR as a percentage, such as 8 for 8%, not 0.08 and not a monthly rate.
• Enter the full repayment term in years. The calculator converts it to months.
• Read total interest as an estimate across all scheduled payments, not as a separate monthly charge.

Changing the term changes both the payment and the total interest calculated. A longer term means more scheduled payments, while a shorter term means fewer. The calculator reports the arithmetic for the inputs; it does not evaluate affordability, eligibility, or whether a particular borrowing choice fits someone’s circumstances.

Common Errors and Limits

A frequent mistake is to treat the APR as the monthly rate. Dividing by 12 converts a percentage rate to a monthly percentage, but the formula needs a decimal, so the conversion is APR ÷ 1,200. Another mistake is to assume that every loan has a fixed rate and identical monthly payments. This calculator models that specific pattern; variable-rate loans, interest-only periods, irregular payment schedules, and loans with balloon payments require different calculations.

The formula also assumes the stated APR is the rate used for monthly interest accrual. Lenders may calculate interest or payment schedules differently, and fees may affect the actual amount financed or total cost. The result is rounded to cents, so the remaining balance after many payments can differ slightly from a lender’s schedule. Extra payments are not included: if a borrower pays more than the scheduled installment, the timing and application of that amount can change the payoff path and interest paid.

Frequently Asked Questions

Does an amortization calculator tell me my exact payment?
It gives an estimate under its stated assumptions. The lender’s payment schedule can differ because of fees, timing, rounding, rate terms, or other loan-specific details.

Is the calculator’s payment principal and interest only?
Yes. This calculator excludes taxes, insurance, PMI, escrow, and fees. Add any separately quoted costs to understand the broader payment obligation, where applicable.

Why does the interest part of a payment change?
Interest is calculated on the outstanding balance. As scheduled payments reduce principal, less interest accrues and a larger share of a level payment goes toward principal.

Can I use it for a variable-rate loan?
Not for a changing rate across the full term. This formula assumes one fixed APR throughout; a variable rate may require recalculation whenever the rate changes.

Does total interest include extra payments?
No. It assumes exactly the scheduled monthly payment for the full term. It does not model additional payments or a shortened payoff period.

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