Amortization Schedule Calculator: Payments and Balance

This amortization schedule calculator estimates a fixed-rate loan’s monthly payment and total interest from the amount borrowed, APR, and term. It also shows how a payment is divided between interest and principal over time; the schedule is an estimate, not a lender’s official disclosure.

Formula

The calculator uses a standard fixed-payment loan formula. It finds a monthly payment that, under the stated assumptions, repays the starting principal and interest over the selected number of monthly payments.

Monthly payment: M = P × r ÷ [1 − (1 + r)⁻ⁿ]

• P is the starting loan principal, in dollars ($).
• APR is the annual percentage rate entered as a percentage.
• r is the monthly rate, calculated as APR ÷ 1,200. For an 8% APR, r = 0.08 ÷ 12.
• n is the number of monthly payments, calculated as loan term in years × 12.
• M is the monthly payment, in dollars. The displayed payment is rounded to cents.

The displayed total interest is calculated as M × n − P, using the calculator’s unrounded payment expression before display rounding. Actual loan statements can differ because lenders apply payment rounding, dates, fees, and other contract terms in their own systems.

Worked Example

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

1. Monthly rate: r = 8 ÷ 1,200 = 0.0066667.
2. Number of payments: n = 5 × 12 = 60.
3. Payment: M = 20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰] = $405.53 per month, rounded to cents.
4. Total of the unrounded scheduled payments: approximately $24,331.88.
5. Estimated interest: $24,331.88 − $20,000 = approximately $4,331.88.

The calculator displays the monthly payment as $405.53 and calculates total interest from the formula’s unrounded payment value. A schedule built from payments rounded to cents can differ by a small amount, often in the final payment.

Assumptions

• The interest rate is fixed for the full term.
• There are equal monthly payments, made at the end of each monthly period.
• Interest accrues monthly using APR divided by 12; this is a simplified periodic-rate model.
• The calculation excludes fees, taxes, insurance, mortgage insurance, escrow, and any other charges or add-ons.
• It assumes no missed, late, extra, or irregular payments, and no changes to the loan terms.

What an Amortization Schedule Shows

An amortization schedule is a dated, payment-by-payment forecast of how a loan balance declines. Each row commonly shows the payment number or date, starting balance, payment amount, interest charged, principal repaid, and ending balance. The balance at the end of one period becomes the starting balance for the next.

For a typical fully amortizing fixed-rate loan, the scheduled payment stays level, but its allocation changes. Interest is calculated on the outstanding balance, so early payments generally contain more interest. As the balance falls, the interest portion falls and more of each unchanged payment reduces principal. By the final scheduled payment, the balance is expected to reach zero, subject to rounding and the lender’s accounting.

How to Read and Use the Results

The monthly payment is the formula’s estimated principal-and-interest installment, not necessarily the full amount due on a bill. Housing payments, for example, may include separately calculated escrow or insurance amounts. Total interest is the estimated interest paid over the entire scheduled term if every payment is made as assumed; it is not the same as the total of payments, which also returns the borrowed principal.

To inspect a specific point in the loan, find that payment’s row in a full schedule. The ending balance is the estimated remaining principal after the payment—not a payoff quote. A payoff amount may also reflect interest accrued since the last payment, fees, or contract-specific calculations. For an actual balance or payoff figure, use the lender’s current statement or request a payoff calculation.

A useful schedule is especially helpful for seeing the timing of principal reduction, comparing the effect of different hypothetical terms or APR inputs, and checking how a planned extra payment might affect repayment. This calculator does not model extra payments; a separate calculation needs the extra amount, when it is applied, and the lender’s treatment of it.

Schedule Requirements and Common Pitfalls

To generate a useful amortization schedule, the basic inputs are the starting principal, interest rate, repayment term, payment frequency, and a clear convention for when interest accrues and payments are applied. A real schedule may also require the first payment date, day-count method, payment rounding, fees financed into the principal, and any variable-rate changes. Those details depend on the loan documents and are not supplied here.

• APR versus periodic rate: Enter APR as a percent, such as 8, not as 0.08. The formula converts it to a monthly rate by dividing by 1,200.
• Years versus months: This calculator accepts years and converts them to months. A term entered in the wrong unit changes the result substantially.
• Rounding: A displayed payment rounded to cents may not reproduce every schedule row exactly. Lenders may adjust the final installment to clear a small remaining balance.
• Fees and add-ons: Charges paid separately are not part of principal here. If a charge is added to the amount borrowed, the principal input would need to reflect that amount.
• Changing terms: Variable rates, skipped payments, late payments, and extra principal payments make the simple fixed schedule inaccurate unless each event is modelled.

Frequently Asked Questions

What information is needed for an amortization schedule?
At minimum, use the starting principal, interest rate, loan term, payment frequency, and assumptions about payment timing and rate changes. A detailed lender schedule may use additional contract-specific dates and rounding rules.

Does an amortization schedule include taxes and insurance?
Not in this calculator. It estimates principal and interest only. Taxes, insurance, escrow, and other charges may affect a bill but are not included unless separately modelled.

Why does more of the payment go to interest at the beginning?
Interest is calculated on the outstanding principal. The balance is largest at the start, so the interest charge generally takes a larger share of each level payment then. As principal is repaid, the interest portion declines.

Is the schedule the same as a payoff amount?
No. A schedule is a projection based on assumptions. A payoff figure can include interest accrued through a particular date and other contract-specific amounts, so check with the lender for an exact figure.

Can an amortization schedule account for extra payments?
A basic fixed-payment schedule cannot unless extra payments are added to the calculation. The amount and timing matter, as does how the lender applies the payment. This calculator does not include them.

Limits of the Estimate

This formula is for a fixed-rate, level-payment loan with monthly periods. It does not determine a lender’s fees, approval terms, variable-rate path, exact payment dates, or contractual balance. Use the lender’s loan documents and disclosure for the actual payment schedule and charges. This result is an estimate, and the lender’s disclosure gives the exact figures.

Related

• Interest Rate Movements: How They Affect Loan Payments
• Interest Rate Meeting Calculator: Estimate Loan Payments
• Mexico Interest Rate: What It Means and 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 | $ | p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2