Amortization Calculator: Fixed Monthly Payment

An amortization calculator works out the fixed monthly principal-and-interest payment needed to repay a loan over a set term, using the loan amount and annual percentage rate (APR). Enter those figures and the term to see the payment and estimated total interest; the calculation assumes a fixed rate and regular monthly payments.

Formula

The fixed monthly payment is the amount that makes the present value of all scheduled payments equal the amount borrowed, assuming a constant monthly interest rate. The formula is:

Payment = P × r / [1 − (1 + r)−n]

• P is the starting loan principal, in dollars.
• r is the monthly interest rate as a decimal: APR ÷ 12 ÷ 100. In the calculator, this is apr / 1200.
• n is the number of monthly payments: loan term in years × 12.

The payment is rounded to the nearest cent. Estimated total interest is calculated as the rounded monthly payment multiplied by the number of payments, minus the original principal. This total assumes every scheduled payment is made as calculated.

Worked Example

Using the calculator’s defaults: a $20,000 loan, 8% APR, and a five-year term:

1. Convert the APR to a monthly decimal rate: 8 / 1200 = 0.0066667.
2. Find the number of monthly payments: 5 × 12 = 60.
3. Substitute into the payment formula: 20,000 × 0.0066667 / [1 − (1.0066667)−60].
4. The monthly payment is $405.53 when rounded to cents.
5. Estimated total interest is $405.53 × 60 − $20,000 = $4,331.80.

The payment covers both interest and principal. Its exact split changes over time even though the scheduled payment stays level.

Assumptions

• The APR and payment amount remain fixed throughout the term.
• Payments are made monthly, with the first payment one month after the loan begins.
• Interest is modelled monthly at APR divided by 12, with no separate daily-interest adjustment.
• The calculation excludes fees, taxes, insurance, PMI, escrow, and any other charges not entered as loan principal.

How a Fixed Payment Amortizes

Amortization means repaying principal through a sequence of payments that also cover interest. For each period, interest is calculated on the outstanding balance. The rest of that period’s payment reduces principal. Because the balance generally falls with each payment, the interest portion usually declines over time and the principal portion grows.

For example, at the start of the default loan, one month’s interest is approximately $20,000 × 0.0066667 = $133.33. From a $405.53 payment, about $272.20 therefore reduces principal. Later, the interest charge is calculated on a smaller balance, so more of the same scheduled payment goes toward principal.

“Fixed payment” describes the regular principal-and-interest amount under these assumptions. A real bill can differ if the loan has a variable rate, fees added to the balance, irregular payment timing, or other components. A mortgage bill, for instance, may include items such as taxes or insurance that this calculation does not include.

When to Use the Calculator

Use the estimate to understand how principal, APR, and term mathematically affect a level monthly payment. It can also help you check a payment figure supplied elsewhere, provided you use the same loan amount, rate, term, payment frequency, and assumptions.

• Enter the amount actually borrowed as principal, not a total that includes charges unless those charges are financed.
• Enter APR as a yearly percentage, such as 8 for 8%, not 0.08 or a monthly rate.
• Enter the term in years. The formula converts it to monthly payments.
• Compare outputs only when the inputs and included costs are on the same basis.

The result is an estimate of scheduled principal and interest, not an approval decision, a full cost quote, or a statement of what a borrower can afford. Obtain the actual APR, payment schedule, and charges from the lender’s disclosure.

Common Errors and Limits

A frequent mistake is confusing APR expressed as a percentage with a decimal rate. The calculator divides the entered percentage by 1,200 to get a monthly decimal rate. For example, 8% becomes 0.0066667 per month; entering 0.08 in the APR field would instead mean 0.08% per year.

Rounding can cause small differences from a lender’s figures. This calculator rounds the monthly payment to cents and uses that rounded payment to estimate total interest. A lender’s schedule may handle the final payment or payment dates differently, or may include fees and other terms. The shown total is not a guarantee that every payment will be identical to the estimate.

The formula does not model extra payments, skipped or late payments, variable rates, changing loan balances, payment-frequency alternatives, or interest calculated using a daily balance. Extra principal payments can change the payoff date and total interest, so a fixed scheduled-payment calculation alone cannot show their effects.

Frequently Asked Questions

Does an amortization calculator show a fixed monthly payment?
Yes. With a fixed APR, a fixed term, and regular monthly payments, it calculates a level principal-and-interest payment. Other bill components or changes to loan terms are not included unless modelled separately.

Why does the interest part of my payment change?
Interest is calculated on the unpaid balance. As principal is repaid, the balance falls, so less interest accrues for a later period and more of the level payment goes toward principal.

Is the calculator’s monthly payment the full loan bill?
Not necessarily. It estimates principal and interest only. Fees, taxes, insurance, PMI, escrow, and other charges can affect an actual bill.

Does a longer loan term lower the monthly payment?
For the same principal and APR, spreading repayment across more monthly payments generally lowers the formula’s scheduled payment, while the loan accrues interest over more periods. The calculator does not determine whether any particular term is suitable.

Why might my lender’s payment differ from this result?
Differences can come from the actual APR, financed fees, payment dates, rounding, a different interest method, or terms not represented here. Compare the calculator inputs with the lender’s written schedule.

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

Related

• JSA First Payment After Interview: What to Expect
• Is Interest Payment a Financing Activity?
• Zero Down Payment First-Time Home Buyer Options

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