Bank Loan Amortization Calculator and Payment Formula

A bank loan amortization calculator estimates the fixed monthly payment and total interest for a fully repaid loan using its principal, annual percentage rate (APR), and term. Enter those three figures to see the payment and interest estimate; the schedule assumes a fixed rate and equal monthly payments.

Formula

For a fixed-rate loan with level monthly payments, the payment is the principal multiplied by the monthly interest rate, divided by one minus the discount factor for all payments:

Payment = P × r / [1 − (1 + r)⁻ⁿ]

• P is the starting loan principal, in dollars.
• r is the monthly interest rate as a decimal: annual APR ÷ 12 ÷ 100.
• n is the number of monthly payments: loan term in years × 12.
• Payment is the unrounded formula result, displayed here to the nearest cent.

Total interest is calculated as the displayed monthly payment multiplied by the number of months, minus the original principal: Total interest = monthly payment × n − P. Since the payment is rounded to cents, this total uses that rounded payment too; an actual final payment or lender schedule can differ slightly because of rounding and payment dates.

Worked Example

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

1. Convert APR to a monthly decimal rate: 8 ÷ 100 ÷ 12 = 0.0066667.
2. Find the number of payments: 5 × 12 = 60.
3. Substitute into the payment formula: $20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰] ≈ $405.53 per month.
4. Calculate total interest using the rounded payment: $405.53 × 60 − $20,000 = $4,331.80.

The estimated payment is $405.53 per month, and estimated total interest is $4,331.80. Multiplying the rounded payment by all 60 months gives total payments of $24,331.80, including repayment of the $20,000 principal.

Assumptions

• The interest rate stays fixed for the full term.
• Payments are equal monthly payments, made at the end of each monthly period.
• Interest compounds monthly using APR divided by 12.
• Fees, taxes, insurance, PMI, escrow, late charges, and payment-date adjustments are not included.

How Amortization Works

Amortization is the gradual repayment of principal and interest through scheduled payments. Early in a standard fixed-payment loan, more of each payment goes toward interest because the balance is larger. As principal is repaid, interest for later periods is calculated on a smaller balance, so more of the same payment reduces principal.

A payment does not normally equal principal divided by months: that simple division leaves out interest. The amortization formula accounts for interest over every payment period and calculates a level payment that pays the modeled balance to zero at the end of the term. For a detailed schedule, each month’s interest is approximately the outstanding balance multiplied by the monthly rate; the remainder of the payment reduces principal.

When to Use the Estimate

Use the calculator to understand the arithmetic of a proposed fixed-payment loan, check how term and APR affect a modeled payment, or estimate the interest implied by the inputs. It can also help you compare hypothetical scenarios on a consistent basis. To make such a comparison meaningful, hold the principal and other assumptions constant and change only the variable you want to examine. This is arithmetic, not a recommendation about borrowing.

Enter the amount actually financed as the principal, not necessarily the advertised purchase price or the amount you hope to receive. Use the APR and term stated in the lender’s documents or quote. If the APR is not yet known, the calculator can illustrate a hypothetical input, but it cannot establish the rate, fees, or approval terms that apply to a real loan.

Reading Results and Common Errors

• APR units: Enter an annual percentage, such as 8 for 8%, not 0.08. The formula converts the percentage to a monthly decimal.
• Term units: Enter years in the term field. A five-year loan means 60 monthly payments, not five payments.
• Payment versus total cost: The monthly payment alone does not show total interest. A longer term may lower the scheduled payment while increasing the number of periods over which interest is charged.
• Rounding: The payment is shown to cents. The lender may round each period differently or adjust the final payment, so a hand-built schedule may not match exactly.
• APR versus periodic rate: The calculator treats APR as a nominal annual rate divided by 12. It does not infer a different compounding convention or model daily interest accrual.

A common misconception is that total interest is simply the stated APR multiplied by the original principal and term. That is not how an amortizing balance behaves: principal declines over time, and each period’s interest is based on the remaining balance under the formula’s assumptions.

Limits and Other Loan Structures

This calculator models a fixed-rate, fully amortizing loan with regular monthly payments. It does not create a lender’s official amortization schedule, quote a rate, or include charges that may be financed or billed separately. Variable-rate loans, interest-only periods, balloon payments, irregular payment dates, deferred payments, and extra principal payments require additional inputs or a different calculation.

If you make extra payments, the balance may be repaid earlier and interest may change, but this calculator does not estimate that effect. Likewise, a loan with a fee or a different payment frequency may have a different effective cost even when its stated principal, APR, and term look similar. Use the lender’s disclosed payment schedule for the contract-specific figures.

Frequently Asked Questions

What does a bank loan amortization calculator show?
It estimates the level monthly payment and, in this calculator, total interest for a fixed-rate loan that is repaid over the entered term.

How do I calculate a monthly loan payment?
Convert annual APR to a monthly decimal rate, determine the number of monthly payments, and use the amortization payment formula shown above. This calculator carries out those steps for the entered values.

Why does the interest portion change each month?
Interest is calculated on the outstanding balance. As payments reduce principal, the balance falls, so the interest portion generally decreases while more of a level payment goes toward principal.

Does this estimate include fees or insurance?
No. It uses only principal, APR, and term. Fees, taxes, insurance, PMI, escrow, and other charges are outside the calculation.

Why might my lender’s payment differ?
The loan may use different terms, payment timing, rounding, financed charges, or interest calculations. Compare the calculator inputs with the lender’s disclosure and schedule.

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