Amortization Schedule Definition and Loan Calculator

An amortization schedule is a table showing how each scheduled loan payment is divided between interest and principal, and how the balance changes over time. This calculator estimates a fixed-rate loan’s monthly payment and total interest from the amount, annual APR, and term; the schedule itself can then be built by applying the same payment and interest calculation to each month.

Formula

The calculator uses the standard level-payment formula for a fixed-rate loan. It first converts the annual percentage rate (APR) to a monthly rate, then calculates the payment needed to repay the original principal over the stated number of monthly payments:

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

• P is the starting loan principal, in dollars.
• r is the monthly interest rate as a decimal: APR ÷ 1,200. For example, 8% APR gives r = 0.08 ÷ 12.
• n is the number of monthly payments: years × 12.

The payment is rounded to cents. The total-interest estimate is the rounded monthly payment multiplied by the number of payments, minus the starting principal: Total interest = payment × n − P. This is a simplified fixed-payment estimate; actual loan statements can reflect different payment dates, rounding practices, fees, or adjustments.

Worked Example

Using the calculator’s defaults—$20,000 principal, 8% annual APR, and a five-year term—the loan has 60 monthly payments. The monthly rate is 0.08 ÷ 12 = 0.0066667.

1. Insert the values into the payment formula: $20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰].
2. The unrounded result is about $405.53, so the monthly payment rounded to cents is $405.53.
3. Multiply that displayed payment by 60: $405.53 × 60 = $24,331.80.
4. Subtract the original principal: $24,331.80 − $20,000 = $4,331.80 total interest.

Because each payment is rounded to cents before the total is calculated, results can differ slightly from a calculation that keeps extra decimal places throughout. A lender’s final payment may also be adjusted to clear a small remaining balance.

Assumptions

• The interest rate remains fixed for the full term.
• Payments are equal, made monthly, and assumed to occur at the end of each monthly period.
• Interest is modelled monthly at APR divided by 12.
• Fees, taxes, insurance, mortgage insurance, escrow, late charges, and extra payments are not included.

How an Amortization Schedule Works

A complete schedule applies the loan’s interest calculation one period at a time. For each month, interest is generally calculated on the outstanding balance. The payment first covers that period’s interest; the remainder reduces principal. The new balance becomes the starting balance for the next row.

For the example, the first month’s interest is approximately $20,000 × 0.08 ÷ 12 = $133.33. From the $405.53 payment, about $272.20 goes toward principal, leaving an estimated balance of $19,727.80. In the next month, interest is calculated on that lower balance. As the balance declines, the interest portion usually shrinks and the principal portion grows, even though the scheduled payment stays level.

A schedule commonly includes the payment number or date, starting balance, payment, interest, principal repaid, and ending balance. The rows should reconcile: starting balance minus principal repaid equals ending balance, subject to rounding. Across the full term, principal repaid should add up to the original amount borrowed.

What the Schedule Helps You See

The schedule makes the timing of repayment visible. It can show how much of the loan remains after a chosen number of payments, how much interest accumulates over the planned term, and why an early payment can be mostly interest even when the payment amount is unchanged. It is also useful for checking whether a quoted payment appears consistent with a stated principal, rate, and term—provided the quote uses the same assumptions.

For a more detailed estimate, calculate each row in sequence using the actual starting balance for that period. With monthly compounding, interest for a regular period is approximately balance × APR ÷ 12. Subtract that interest from the payment to get principal repaid, then subtract principal from the starting balance. Do not assume that the calculator’s total-interest output is a lender payoff quote: payoff amounts can depend on the date and accrued interest since the latest payment.

Common Misunderstandings and Limits

• Payment is not the same as principal reduction. Part of each payment covers interest, particularly while the balance is high.
• APR and monthly rate are not interchangeable. Enter APR as a percentage per year; the formula divides it by 1,200 to get a monthly decimal rate.
• Term affects total interest. Holding principal and rate fixed, a longer repayment period generally means more scheduled payments and more interest overall, although the payment is lower.
• Extra payments change the schedule. If an additional amount is applied to principal, later interest and the payoff timing can change. The calculator does not model that activity.
• Variable rates do not follow one fixed schedule. If a rate changes, future interest and payments may differ from the original projection.

Actual contracts may use daily interest accrual, irregular first periods, payment-date conventions, or other calculation details. Check the loan’s payment terms and use the lender’s figures when exact amounts matter. The APR and loan amount should be entered using the figures applicable to the loan being examined; the calculator does not supply or predict them.

Frequently Asked Questions

What does an amortization schedule show?
It shows each planned payment’s interest and principal portions, along with the remaining loan balance after that payment.

Does amortization mean the loan payment stays the same?
For a standard fixed-rate, level-payment loan, the scheduled payment is generally constant. The share going to interest versus principal changes over time. Other loan structures may work differently.

Why does the early part of a schedule show more interest?
Interest is calculated on the outstanding balance. The balance is largest at the beginning, so the interest charge is usually largest then; as principal is repaid, that charge tends to fall.

Can I use an amortization schedule for extra payments?
A basic schedule assumes only the stated regular payments. To model extra payments, add them to the appropriate period’s principal reduction and recalculate later balances; confirm how the lender applies extra funds.

Is an amortization schedule the same as a payoff quote?
No. A schedule is a projection based on assumptions and regular payment timing. A payoff quote is tied to a specific date and may include accrued interest or other amounts not represented here.

This result is an estimate; the lender’s disclosure gives the exact figures.

Related

• Interest Rate Predictions: What Borrowers Should Know
• Prime Interest Rate: Meaning and How It Works
• Interest Rate Parity: Meaning, Formula and Example

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