Payment Amortization Calculator: Monthly Payment & Interest

A payment amortization calculator estimates the fixed monthly payment and total interest for a loan repaid in equal monthly installments. Enter the loan amount, annual percentage rate (APR), and term in years to see the payment and the total interest calculated from it.

Formula

The calculator uses the standard fixed-payment amortization formula. It first calculates the monthly payment, rounds it to the nearest cent, and then estimates total interest by subtracting the amount borrowed from all scheduled payments.

Monthly payment: M = round(P × r ÷ [1 − (1 + r)⁻ⁿ], 2), where r = APR ÷ 1200 and n = years × 12.

Total interest: I = M × n − P.

• P is the starting loan principal, in dollars.
• APR is the annual percentage rate entered as a percentage, such as 8 for 8% per year.
• r is the monthly interest rate as a decimal. Dividing the percentage APR by 1,200 converts it to a monthly decimal rate.
• n is the number of monthly payments.
• M is the monthly payment, in dollars.
• I is estimated total interest over the full scheduled term, in dollars.

This calculation assumes the same payment is made once per month and applies a fixed monthly rate to the remaining balance. The displayed interest uses the cent-rounded payment, so it reflects the payment shown rather than an unrounded theoretical amount.

Worked Example

Using the calculator’s default inputs—$20,000 principal, 8% APR, and a five-year term—there are 5 × 12 = 60 monthly payments. The monthly rate is 8 ÷ 1,200 = 0.0066667.

1. Calculate the payment factor: (1 + 0.0066667)⁻⁶⁰ ≈ 0.6712.
2. Calculate the payment: $20,000 × 0.0066667 ÷ (1 − 0.6712) ≈ $405.53 per month after rounding to cents.
3. Calculate total interest using the displayed payment: $405.53 × 60 − $20,000 = $4,331.80.

The result is an estimated monthly payment of $405.53 and estimated total interest of $4,331.80. Actual loan schedules can differ by cents because lenders may use different payment dates, rounding practices, or final-payment adjustments.

Assumptions

• The interest rate remains fixed for the entire term.
• Payments are equal, made monthly, and paid at the end of each monthly period.
• Interest compounds monthly using APR divided by 12.
• The estimate excludes fees, taxes, insurance, PMI, and escrow because they are not calculator inputs.

When to Use an Amortization Calculator

Use the estimate to understand how the principal, rate, and term mathematically affect scheduled payments and interest. It can also help you review hypothetical loan amounts or terms. The entered APR and other loan figures should come from the lender’s written quote or disclosure; this calculator does not supply or predict rates, fees, or eligibility.

An amortizing loan pays down principal over time. Each payment covers interest accrued for that period and applies the remainder to principal. Early in a typical fixed-rate schedule, the balance is larger, so more of the payment goes toward interest. As principal falls, the interest portion usually declines and the principal portion grows. The scheduled payment stays level in this simplified model.

How to Read the Results

The monthly payment is the modeled principal-and-interest installment, not necessarily the full amount due each month. For a mortgage, for example, taxes, insurance, mortgage insurance, or escrow collections may be billed separately or included in a lender’s payment quote. Check which components a quoted payment includes before comparing it with this result.

Total interest is the sum of modeled payments minus the original principal. It is not the total amount paid: the modeled total paid is the principal plus interest. In the example, that is $24,331.80. It also is not a measure of fees or the total cost of borrowing when other charges apply.

Common Mistakes and Limits

• Entering APR in the wrong form: Enter 8 for 8%, not 0.08. The formula converts the percentage to a monthly decimal rate.
• Confusing years and months: The term field is in years; the formula multiplies it by 12 to obtain the number of payments.
• Treating the result as a complete bill: The output excludes costs that are not inputs, such as fees, taxes, and insurance.
• Assuming every loan is fixed-rate: A variable-rate loan can change its payment or total interest when its rate changes, so this fixed-rate estimate will not model later adjustments.
• Ignoring rounding: The monthly payment is rounded to cents. The lender’s schedule may adjust the final installment or show a slightly different total due to its calculation and posting conventions.

The formula is for a fully amortizing loan with regular monthly payments and a positive APR. It does not model interest-only periods, irregular payment dates, extra principal payments, skipped payments, balloon payments, rate changes, or fees financed into the loan. To model any of those features, the relevant terms and timing must be included in a more detailed schedule.

Frequently Asked Questions

What does a payment amortization calculator show?
It estimates the level monthly principal-and-interest payment and the total interest over the entered term, based on the loan amount and APR.

Does the monthly payment include taxes and insurance?
No. This calculator only estimates principal and interest. Taxes, insurance, PMI, escrow, and fees are not included.

Why does the interest portion change if the payment stays the same?
Interest is calculated on the outstanding balance. As payments reduce principal, the balance used to calculate later interest becomes smaller.

Can I use this calculator for a variable-rate loan?
It can show a hypothetical estimate if you enter one rate, but it assumes that rate stays fixed throughout the term and cannot forecast future rate changes.

Does paying extra reduce total interest?
Extra principal payments can reduce a balance sooner and therefore may reduce interest, but this calculator assumes only the scheduled fixed payment. It does not calculate an extra-payment schedule.

Why might a lender’s payment differ?
A lender’s figure may include additional charges or use different payment dates, rounding, or contract terms. Use the lender’s disclosure for the exact scheduled figures.

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

Related

• Amortization Schedule by Payment Amount: How It Works
• Amortization Calculator With Payment Input
• Amortization Formula With Extra Payments: How It Works

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