Free Loan Amortization Calculator and Payment Schedule

This free loan amortization calculator estimates a fixed-rate loan’s monthly payment and total interest from the amount borrowed, annual APR, and term. Enter those three figures to see the results; the calculation assumes monthly payments and shows the standard level-payment estimate.

Formula

The monthly payment uses the fixed-rate amortizing-loan formula:

Payment = P × r ÷ [1 − (1 + r)⁻ⁿ]

• P is the principal, or amount borrowed, in dollars.
• r is the monthly interest rate, calculated as APR ÷ 1,200. APR is entered as a percentage per year; for example, 8% gives a monthly rate of 0.0066667.
• n is the number of monthly payments, calculated as the term in years × 12.

Total interest is estimated as monthly payment × n − P. The calculator’s displayed payment and interest are rounded to cents. The formula assumes the payment remains level and that the loan is paid through the scheduled monthly installments.

Worked Example

Using the calculator’s default inputs—$20,000 principal, 8% annual APR, and a 5-year term:

1. Convert the APR to a monthly rate: 8 ÷ 1,200 = 0.0066667.
2. Convert the term to payments: 5 × 12 = 60 months.
3. Substitute into the payment formula: $20,000 × 0.0066667 ÷ [1 − (1 + 0.0066667)⁻⁶⁰] ≈ $405.53 per month, rounded to cents.
4. Estimate total interest using the rounded payment: $405.53 × 60 − $20,000 = $4,331.80.

These are estimates from the stated formula and assumptions. A lender’s schedule may differ if its payment dates, rounding, fees, or interest calculation differ.

Assumptions

• The interest rate is fixed for the full term.
• Payments are level monthly installments, made at the end of each monthly period.
• Interest compounds monthly at APR ÷ 12.
• Fees, taxes, insurance, PMI, and escrow are not included.

How Amortization Works

Amortization means repaying principal and interest through a sequence of scheduled payments. Early in a fully amortizing loan, a larger share of each payment generally goes toward interest because the outstanding balance is larger. As the balance falls, the interest portion usually declines and more of each level payment goes toward principal. The payment remains the same in this simplified model, but its components change.

An amortization schedule lists the opening balance, interest charged, principal repaid, and closing balance for each period. To estimate one month’s interest, multiply the opening balance by the monthly rate. Subtract that interest from the payment to find the principal portion, then subtract the principal portion from the opening balance. For example, at the default rate, first-month interest is approximately $20,000 × 0.0066667, or $133.33. The remaining portion of the $405.53 payment—about $272.20—reduces principal.

When to Use the Estimate

This calculator can help you understand the payment-and-interest arithmetic for a proposed fixed-rate loan or compare hypothetical amounts, rates, and terms on a consistent basis. It does not determine whether a loan is appropriate, what payment fits a budget, or whether a borrower will be approved. Use the APR and loan details supplied for the specific loan; do not treat the example defaults as a current market rate or quote.

A shorter term generally means fewer scheduled payments, while the payment formula spreads repayment over fewer months. A longer term spreads principal over more payments. The resulting payment and total interest depend on the principal, rate, term, and the calculator’s assumptions. Change one input at a time if you want to see how that input affects the mathematical estimate.

Reading Results and Common Limitations

Monthly payment is the estimated amount of each scheduled principal-and-interest installment. It is not necessarily the full amount due each month: a real loan may have separate charges or payment components. Total interest is the estimated interest over all scheduled payments, not the total amount repaid. Add the principal to the displayed interest to estimate the total of the modeled payments.

• APR versus interest rate: APR can reflect certain costs in addition to the nominal interest rate, depending on how the lender presents the figures. This calculator treats the entered APR as the rate used in the monthly interest formula; it does not separately model fees.
• Rounding: The formula rounds the payment to cents for display, and the total-interest calculation uses that rounded payment. A lender may round each period differently, so small discrepancies can accumulate.
• Payment timing: The calculation assumes regular monthly periods. A first payment date that is unusually early or late can affect interest and the actual schedule.
• Variable rates and irregular payments: A changing rate, skipped or late payment, extra principal payment, or payoff before the term ends changes the schedule and is not represented by this fixed-payment result.

For an exact schedule, check the lender’s loan disclosure or payment schedule, including how it handles payment dates, fees, and rounding. This calculator does not replace those loan-specific figures.

Frequently Asked Questions

What does a loan amortization calculator show?
It estimates a fixed monthly principal-and-interest payment and, here, the total interest across the entered term. A full amortization schedule also breaks each payment into interest and principal and shows the remaining balance over time.

Does total interest include the amount borrowed?
No. Total interest is the estimated cost of interest alone under the formula. To estimate total scheduled payments, add the principal to total interest.

Why is my lender’s payment different?
Possible reasons include a different rate basis, payment date, loan term, fee treatment, payment rounding, or additional charges. Confirm that the principal, APR, and term you entered match the lender’s figures, then consult the lender’s disclosure for its calculation.

Can I use this for a variable-rate loan?
Only as a snapshot under a single assumed rate. The calculator holds the rate constant, so it cannot forecast payments or total interest after future rate changes.

Does this include extra payments?
No. The estimate assumes only the regular scheduled payment. Extra payments can change the balance and payoff timing; this calculator does not model them.

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