Loan Amortization Schedule: Formula and Example

This calculator estimates the monthly payment and total interest for a fixed-rate, fully amortizing loan, using the loan amount, annual percentage rate (APR), and term you enter. It also helps explain how payments reduce the balance over time; the displayed payment is rounded to cents, as real payment schedules commonly are.

Formula

An amortization schedule is a table showing how each scheduled loan payment is divided between interest and principal, and how the remaining principal balance changes. To calculate the level monthly payment for a fixed-rate loan, use:

Payment = P × r ÷ [1 − (1 + r)⁻ⁿ]

• P is the starting principal, in dollars.
• r is the monthly interest rate as a decimal: APR ÷ 1,200.
• n is the number of monthly payments: years × 12.
• Payment is the regular monthly payment, in dollars.

The calculator’s total interest is the rounded monthly payment multiplied by the number of payments, minus the starting principal: Total interest = payment × n − P. This assumes the rounded payment is made for every installment and the balance is paid off at the end. A lender’s actual schedule may handle the final payment or rounding differently.

Worked Example

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

1. Convert the annual rate to a monthly decimal: 8 ÷ 1,200 = 0.0066667.
2. Find the number of monthly payments: 5 × 12 = 60.
3. Apply the payment formula: $20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰] = $405.53 when rounded to cents.
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.

Assumptions

• The rate is fixed for the full term.
• Payments are equal monthly installments, made at the end of each monthly period.
• Interest accrues monthly at APR ÷ 12; the calculation treats the APR as a nominal annual rate.
• The estimate excludes fees, taxes, insurance, PMI, and escrow because they are not inputs.

How to Read an Amortization Schedule

A full schedule usually has one row per payment, with columns for the payment number or date, amount paid, interest, principal, and remaining balance. For each period, interest is calculated on the balance outstanding at the start of that period. The principal portion is the payment minus that period’s interest; subtracting it from the previous balance gives the new balance.

For example, with the default figures, the first month’s interest is approximately $20,000 × 0.08 ÷ 12 = $133.33. From a $405.53 payment, about $272.20 therefore goes to principal. The balance falls to approximately $19,727.80. Later interest charges are smaller as the balance declines, so a larger share of the unchanged payment goes to principal. Small differences in a displayed schedule can result from rounding each monthly amount to cents.

The calculator above gives the payment and total interest, not every dated row of the schedule. To construct a month-by-month estimate, repeat the interest and balance calculations for each payment period. The opening balance for one row is the preceding row’s closing balance.

When It Is Useful—and What It Leaves Out

A schedule can help a borrower understand the planned repayment path, check how much of a payment initially covers interest, and see the projected balance at different points in the term. It is also a way to compare the arithmetic of different loan amounts, rates, or terms when those inputs are known. Enter the figures supplied for the specific loan; the example rate is only an input for illustration, not a statement about available rates.

The schedule describes the loan under its stated assumptions, not necessarily every amount due on a bill. A payment that includes escrow, insurance, taxes, or fees can exceed the scheduled principal-and-interest payment. Variable rates, irregular payment dates, payment holidays, late amounts, fees added to the balance, and extra payments can also make the actual path differ. For exact amounts and timing, use the lender’s loan disclosure or servicing information.

Common Misconceptions and Calculation Limits

• “Amortization” does not mean interest is split evenly. The total payment is level in this model, but its interest and principal parts change over time.
• APR is not entered as a decimal percentage. Enter 8 for 8%, not 0.08. The formula divides the annual percentage by 1,200 to get a monthly decimal.
• Total interest is not the same as total paid. Total paid is the sum of payments; total interest excludes the principal repaid.
• Extra principal payments change the schedule. They generally reduce the balance used for later interest calculations, but the timing and treatment depend on the loan terms. This calculator does not model them.

This formula applies to level-payment, fully amortizing loans with a fixed rate and monthly periods. It does not model interest-only periods, balloon payments, changing rates, or payment schedules that use a different compounding convention. Because the payment is rounded to cents, a real final installment can differ slightly from the estimate.

Frequently Asked Questions

What does an amortization schedule show?
It lists scheduled payments and shows, for each period, the amount allocated to interest and principal and the remaining loan balance.

How is a loan payment calculated from an amortization schedule?
For a fixed rate and equal monthly payments, use the principal, monthly rate, and total number of payments in the level-payment formula shown above. The schedule then breaks each payment into interest and principal.

Why does more of my payment go to interest at the beginning?
Interest for a period is based on the balance at its start. The balance is largest at the beginning, so the interest portion is usually larger then; as principal is repaid, the interest portion declines.

Does an amortization schedule include taxes and insurance?
Not necessarily. A principal-and-interest schedule excludes them unless they are explicitly included in the calculation. Escrow or other billed costs may appear separately in a payment statement.

Does paying extra change the amortization schedule?
Extra payments applied to principal can reduce the outstanding balance and later interest, changing the schedule. The result depends on when the extra amount is paid and how the servicer applies it; this calculator assumes regular payments only.

Term Origin and Usage

Amortization schedule is standard financial terminology, not slang or an informal expression. Amortization comes through French from Latin roots meaning to extinguish or render dead; in finance, it refers to paying down a debt over time through installments. Schedule refers to an organized list or timetable. In ordinary loan discussions, the phrase names the payment-by-payment table, as in: “The lender provided an amortization schedule showing the projected balance after each monthly payment.” Exact figures depend on the loan contract and payment history. This result is an estimate; 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