Amortization Loan Payment Calculator and Formula

An amortization loan payment calculator estimates the fixed monthly payment needed to repay a loan over a stated term, then shows the total interest implied by that payment. Enter the loan amount, annual interest rate (APR), and term in years; the results assume monthly payments and a fixed rate.

Formula

The calculator uses the standard fixed-payment amortization formula. It converts APR to a monthly rate, calculates the payment that brings the balance to zero after the planned number of payments, rounds that payment to cents, and estimates interest as all scheduled payments minus the original principal.

Monthly payment: M = round[P × r ÷ (1 − (1 + r)⁻ⁿ), 2]. Total interest: I = M × n − P.

• P is the amount borrowed, in dollars.
• APR is the annual percentage rate entered as a percentage; r = APR ÷ 1200 is the monthly rate as a decimal.
• n is the number of monthly payments, calculated as loan term in years × 12.
• M is the monthly payment, in dollars, rounded to the nearest cent.
• I is estimated total interest, in dollars, calculated using the rounded monthly payment.

The payment formula spreads principal and interest across the full schedule. Early payments generally contain a larger interest share because interest is calculated on a larger outstanding balance. As principal falls, the interest portion falls and more of each level payment reduces principal.

Worked Example

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

1. Convert the annual rate to a monthly decimal: r = 8 ÷ 1200 = 0.0066667.
2. Find the number of payments: n = 5 × 12 = 60.
3. Substitute into the payment formula: M = round[20,000 × 0.0066667 ÷ (1 − (1.0066667)⁻⁶⁰), 2] = $405.53 per month.
4. Calculate total interest using the rounded payment: I = $405.53 × 60 − $20,000 = $4,331.80.

The scheduled payments total $24,331.80, of which $20,000 is principal and $4,331.80 is estimated interest. Actual account figures can differ if payment dates, rounding, fees, or the lender’s calculation method differ.

Assumptions

• The interest rate stays fixed for the entire term.
• Payments are equal monthly installments, made at the end of each monthly period.
• Interest accrues monthly at APR divided by 12, with no separate daily-accrual adjustment.
• The calculation excludes fees, taxes, insurance, PMI, and escrow; none of these are inputs.

When to Use the Calculator

Use an amortization payment estimate to understand the principal-and-interest payment implied by a particular amount, rate, and term. You can change one input at a time to see how the scheduled payment responds. A longer term usually lowers the required monthly payment under the same rate and principal, but it also means more payment periods; the interest total shown here helps make that trade-off visible within the formula’s assumptions.

The result is not a complete household budget or a statement about approval. For a loan offer, use the exact amount, APR, term, and payment details in the lender’s disclosure. If the loan has a variable rate, a balloon payment, deferred interest, or a changing repayment schedule, a fixed-payment calculation will not reproduce that structure.

How to Read an Amortization Schedule

An amortization schedule lays out each payment period, showing the payment, interest charged, principal repaid, and remaining balance. For a simple monthly schedule, interest for a period is approximately the opening balance multiplied by the monthly rate. The principal portion is the payment minus that period’s interest, and the next balance is the prior balance minus principal repaid.

For example, at the start of the default example, monthly interest on $20,000 at 0.0066667 is about $133.33. From a $405.53 payment, about $272.20 goes toward principal. In later months, the balance is lower, so the interest portion declines. The calculator provides the payment and aggregate interest, not every row of the schedule.

Common Mistakes and Limits

• Entering a monthly rate as APR: Enter the annual percentage rate, such as 8 for 8%, not 0.6667 for an assumed monthly percentage. The calculator divides the APR by 1,200.
• Confusing years and months: The term field is in years. A five-year term creates 60 monthly payments.
• Treating payment as total housing or borrowing cost: The result covers principal and modeled interest only. Applicable costs outside those inputs are not included.
• Assuming the final balance is exact to the cent: The payment is rounded to cents, so applying that rounded payment over every period can leave a small difference that a lender may handle in the final installment.

The formula requires a positive rate and a positive term. The calculator accepts APR from 0.01% through 100% and terms from 0.0833 through 50 years; these are calculator input boundaries, not statements about available loan terms. A zero-interest loan needs a different formula: payment equals principal divided by the number of payments. This calculator does not model that case.

Frequently Asked Questions

What does an amortization loan payment calculator show?
It estimates a level monthly principal-and-interest payment for a fixed-rate loan and calculates total interest across the stated term using that rounded payment.

How do I calculate a loan payment by hand?
Convert APR to a monthly decimal by dividing by 1,200, convert years to months by multiplying by 12, and substitute those values and principal into the payment formula above. Round the resulting payment to cents.

Does the monthly payment include taxes and insurance?
No. This calculation includes modeled principal and interest only. Taxes, insurance, PMI, escrow, and fees are excluded unless separately added outside the calculator.

Why does a longer loan term change total interest?
A longer term creates more monthly payment periods. With a positive rate, interest accrues across those periods, so the total-interest estimate can rise even when the scheduled monthly payment falls.

Why might a lender’s payment differ from this estimate?
The lender may use different payment dates, rounding, accrual conventions, included charges, or loan terms. Compare the same principal, APR, and repayment schedule, and refer to the lender’s disclosure for its figures.

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