Loan Amortization Calculator by Payment Amount

A loan amortization calculator based on payment amount shows how a fixed payment reduces a loan balance over time and how much interest accrues. Enter the loan amount, annual percentage rate (APR), and term to calculate the scheduled monthly payment and total interest; to model a different payment amount, compare that amount with the calculated payment or use a calculator that accepts payment as an input.

Formula

This calculator uses the standard fixed-payment amortization formula. It first calculates the monthly payment needed to repay the principal and interest in the entered number of months, then subtracts the original principal from all scheduled payments to estimate total interest.

• r = monthly interest rate, calculated as APR ÷ 1,200 when APR is entered as a percentage.
• n = number of monthly payments, calculated as loan term in years × 12.
• P = starting loan principal, in dollars.
• M = monthly payment, in dollars.
• I = total scheduled interest, in dollars.

Monthly payment: M = P × r ÷ [1 − (1 + r)⁻ⁿ]. The calculator displays the result to the nearest cent. Total interest: I = M × n − P, using the displayed, cent-rounded payment. The APR input is divided by 1,200 to convert a percentage per year to a decimal rate per month.

Worked Example

Using the defaults—$20,000 principal, 8% APR, and a five-year term—the loan has 60 monthly payments. The monthly rate is 8 ÷ 1,200 = 0.0066667, or about 0.66667%.

1. Substitute the values: M = 20,000 × 0.0066667 ÷ [1 − (1 + 0.0066667)⁻⁶⁰].
2. The payment before rounding is about $405.53, so the monthly payment displayed is $405.53.
3. Multiply that rounded payment by 60: $405.53 × 60 = $24,331.80 in scheduled payments.
4. Subtract the original $20,000 principal: $24,331.80 − $20,000 = $4,331.80 total interest.

Assumptions

• The APR stays fixed for the entire term.
• Payments are equal, made monthly, and applied at the end of each monthly period.
• Interest compounds monthly at APR divided by 12.
• The calculation excludes fees, taxes, insurance, private mortgage insurance, and escrow because none is entered as an input.
• The term is treated as a whole number of monthly payments; actual contracts may use different payment dates, rounding, or final-payment adjustments.

How a Payment-Based Amortization Calculator Works

An amortization schedule divides each payment between interest and principal. In a standard fixed-rate loan, interest for a period is calculated on the balance at the beginning of that period. The remainder of the payment reduces principal. As the balance falls, the interest portion generally declines and the principal portion rises, while the scheduled payment remains level.

For example, with the default monthly rate, the first month’s interest is approximately $20,000 × 0.0066667, or $133.33. From the $405.53 payment, about $272.20 therefore goes toward principal. Later payments use the then-current balance, so their interest portions differ. A full schedule repeats this calculation month by month; the calculator’s total-interest figure summarizes the schedule rather than listing every row.

The calculator here derives the payment from the amount borrowed, rate, and term. That distinction matters because “based on payment amount” can also mean starting with a payment the borrower supplies and calculating payoff time. This page does not take a custom payment as an input, so it cannot determine a payoff date for an arbitrary payment. Its result is the level payment consistent with the three entered loan terms.

When to Use the Result

Use the estimate to understand the arithmetic of a fully amortizing loan or to compare scenarios by changing one input at a time. For instance, a longer term generally spreads repayment across more months, changing both the required payment and the total interest under the formula. A different APR also changes the monthly interest calculation. These are mathematical effects, not a determination of eligibility, suitability, or affordability.

To explore a payment amount you already have in mind, compare it with the calculated scheduled payment only as a starting point. A payment below the interest accruing for a period may fail to reduce principal; a payment above the scheduled amount may reduce it faster if the contract allows extra principal payments and the extra is applied that way. This calculator does not model extra payments, payment restrictions, or their timing. A separate payoff calculator needs the custom payment amount and may also need the lender’s rules for applying it.

Common Sources of Differences

• APR versus monthly rate: Enter APR as a percentage such as 8, not as 0.08. The formula divides the entered percentage by 1,200.
• Term units: The term field is in years. Five means 60 monthly periods, not five payments.
• Payment rounding: The displayed payment is rounded to cents, and total interest uses that rounded amount multiplied by the number of payments. A real lender may adjust the final payment to clear a small remaining balance.
• Fees and financed costs: If fees are added to the amount borrowed, the principal used in the calculation should reflect that amount. Fees paid separately are not included here.
• Variable rates or irregular schedules: The formula assumes a constant rate and equal monthly periods. Rate changes, skipped payments, daily-interest methods, and unusual payment dates can produce different results.

It is also a misconception that the APR alone always reproduces every amount on a loan disclosure. This calculator treats the entered APR as the nominal annual rate used to calculate monthly interest. Contract terms, fees, compounding conventions, and payment timing can affect disclosed figures, and are not separately represented by the inputs.

Frequently Asked Questions

Can I enter my own monthly payment?
No. This calculator finds the scheduled payment from principal, APR, and term. A custom-payment payoff calculation requires a different formula and an input for the payment amount.

Does the monthly payment include taxes and insurance?
No. It estimates principal and interest only. Taxes, insurance, mortgage insurance, escrow, and fees are excluded unless included in the principal or otherwise represented in a separate calculation.

Why can my lender’s payment differ?
The lender may use different contract details, payment dates, rounding, fees, or rate conventions. Check the loan disclosure for the actual scheduled amount and terms.

Does making extra payments reduce the total interest?
Extra principal payments can change the balance and interest path if the contract permits them and they are applied to principal. This calculator assumes only the scheduled level payments and does not estimate that effect.

What happens if the interest rate changes?
This calculation assumes a fixed APR. A changing rate requires recalculating the payment or balance for each period using the applicable rate and the loan’s contract terms.

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