Loan Amortization Calculator Monthly Payment

A loan amortization calculator works out the fixed monthly payment needed to repay a loan over a chosen term, plus the estimated total interest. Enter the loan amount, annual percentage rate (APR), and term in years to see the payment and interest under a standard fixed-rate repayment formula.

Formula

The standard fixed-payment amortization formula converts the annual rate to a monthly rate, then calculates the level payment that reduces the balance to zero over the scheduled number of payments:

M = P × r ÷ [1 − (1 + r)⁻ⁿ]

• M is the monthly payment in dollars.
• P is the starting loan principal in dollars.
• r is the monthly interest rate as a decimal: APR ÷ 1,200. For an APR of 8%, r = 0.0066667.
• n is the number of monthly payments: loan term in years × 12.

The calculator displays the payment to the nearest cent. It then estimates total interest as the rounded monthly payment multiplied by the number of months, minus the original principal. Using the displayed payment in that total keeps the calculation consistent with the scheduled amount shown.

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.

Substitute those values into the payment formula:

M = 20,000 × 0.0066667 ÷ [1 − (1 + 0.0066667)⁻⁶⁰]

The unrounded result is about $405.53 per month; rounded to cents, the estimated payment is $405.53. Total scheduled payments are $405.53 × 60 = $24,331.80. Subtracting the $20,000 principal gives estimated total interest of $4,331.80.

Assumptions

• The interest rate stays fixed for the entire term.
• Payments are made monthly, at the end of each period, with the first payment one month after the loan starts.
• Interest is modelled monthly using APR divided by 12.
• The calculation does not include fees, taxes, insurance, PMI, escrow, late charges, or other costs unless they are already included in the principal or rate you enter.
• It assumes each scheduled payment is made in full and on time, with no extra payments or changes to the balance.

How Amortization Changes the Balance

Amortization is the gradual repayment of principal through scheduled payments. Each payment covers interest accrued since the previous payment; whatever remains reduces principal. Because interest is calculated on the outstanding balance, the interest portion generally declines as the balance falls, while the principal portion grows. With a fixed rate and payment, the payment itself stays level in this model.

For example, at the start of the default loan, monthly interest is approximately $20,000 × 0.0066667, or $133.33. Of the $405.53 payment, about $272.20 therefore goes toward principal. Later payments have a smaller interest portion if payments are made as scheduled. The exact allocation can differ when a lender uses different timing, rounding, or accrual conventions.

The total-interest output is not an extra monthly bill. It is the estimated sum of interest across the full scheduled term. The monthly payment is also not necessarily the full amount due on an account: separate charges or payment components may apply.

When to Use the Estimate

Use the calculator to understand how principal, rate, and term interact before comparing a calculation with written loan details. It can also help explain a payment quote: enter the quoted principal, APR, and term, then check whether the resulting scheduled payment is in the same range. The calculator does not establish what rate, fees, or loan terms apply; obtain those figures from the lender’s disclosure.

Changing one input at a time makes the effect easier to see. A larger principal generally raises the payment. A higher APR raises the payment and total interest. A longer term usually reduces the required monthly payment but means more payment periods; with a positive rate, that often increases total interest. These are mathematical effects under the stated assumptions, not a recommendation about which loan terms to choose.

Common Calculation Problems and Limits

• Entering the wrong rate unit: Enter an annual APR as a percentage, such as 8 for 8%, not 0.08. The calculator divides the percentage by 1,200 to obtain a monthly decimal rate.
• Confusing years and months: The term field is in years. A five-year term means 60 monthly payments, not five payments.
• Comparing different loan amounts: A payment quote is meaningful only alongside the principal, APR, term, and included charges used to calculate it.
• Assuming every payment is principal repayment: Early payments include interest, so the balance does not fall by the full payment amount.
• Expecting exact lender figures: Daily interest accrual, payment dates, fees, rounding rules, variable rates, and irregular first periods can change actual amounts.

This formula is for a fully amortizing loan with a positive fixed APR and equal monthly payments. It does not model an interest-only period, a balloon payment, a variable rate, skipped payments, or extra principal payments. For a variable-rate loan or a payment schedule that changes, a single fixed-rate estimate cannot show the complete repayment path.

Frequently Asked Questions

How do I calculate a loan’s monthly payment?
Convert APR to a monthly decimal by dividing it by 1,200, multiply the principal by that monthly rate, then divide by 1 minus (1 plus the monthly rate) raised to the negative number of monthly payments. Round the result to cents.

Does an amortization calculator include interest?
Yes. The payment formula includes interest, and this calculator also estimates total interest over the scheduled term. It does not automatically include separate fees, insurance, taxes, or escrow.

Why does the interest part of my payment change?
Interest is calculated against the outstanding balance. As scheduled payments reduce principal, less interest accrues in later periods, leaving a larger share of the level payment to reduce principal.

Does a longer loan term lower the monthly payment?
For the same principal and positive fixed APR, spreading repayment over more months generally lowers the required monthly payment. It also creates more payment periods, so the total interest can be higher.

Why does the calculator differ from my lender’s payment?
The lender may include financed charges or use different rate, date, accrual, or rounding details. Confirm the principal, APR, term, payment schedule, and included costs in the lender’s disclosure.

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