Loan Amortization Graph: Payment and Balance Calculator

A loan amortization graph shows how each scheduled payment is divided between interest and principal, and how the remaining balance falls over time. Enter a loan amount, APR, and term below to calculate the monthly payment and total interest; the graph can then be read alongside those figures to understand the repayment path.

Formula

For a fixed-rate loan with equal monthly payments, the scheduled payment is calculated using the standard amortization formula:

Payment = P × r / [1 − (1 + r)⁻ⁿ]

• P is the starting principal, in dollars.
• r is the monthly interest rate as a decimal: APR ÷ 1200.
• n is the total number of monthly payments: years × 12.
• Payment is the monthly amount, rounded to the nearest cent.

Total interest in this calculator is the sum of the rounded monthly payments minus the original principal: total interest = payment × n − P. Because the payment is rounded to cents, the final scheduled payment may need a small adjustment in an actual loan account. The simple total-interest calculation assumes the displayed regular payment is made for every month.

Worked Example

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

1. Convert the annual percentage rate to a monthly decimal: 8 ÷ 1200 = 0.0066667.
2. Find the number of payments: 5 × 12 = 60.
3. Substitute the values: payment = 20,000 × 0.0066667 ÷ [1 − (1 + 0.0066667)⁻⁶⁰].
4. The unrounded payment is about $405.53, so the monthly payment rounded to cents is $405.53.
5. Total interest using that rounded payment is $405.53 × 60 − $20,000 = $4,331.80.

Assumptions

• The interest rate is fixed for the full term.
• Payments are equal, made monthly, and treated as occurring at the end of each monthly period.
• Interest compounds monthly using APR divided by 12.
• Fees, taxes, insurance, private mortgage insurance, escrow, and any payment changes are not included.

How to Read an Amortization Graph

A typical loan amortization graph has time along the horizontal axis and dollars along the vertical axis. It may show the outstanding balance as a line, with separate stacked bars or lines for principal and interest paid in each period. The balance line generally declines toward zero when scheduled payments fully repay the loan.

At the start of a standard fixed-rate loan, the balance is highest, so the interest calculated for that month is also relatively large. As principal is repaid, later interest charges are calculated on a smaller balance. With a level payment, that usually means a larger share of each payment goes to principal as the loan progresses. It does not mean the interest rate itself is gradually falling.

For the example above, the first month’s interest is approximately $20,000 × 0.0066667, or $133.33. Of the $405.53 payment, about $272.20 therefore reduces principal. The next month’s interest is calculated on the slightly lower balance, subject to the lender’s exact rounding and posting methods.

What the Graph Can and Cannot Show

An amortization graph is a visual summary of a payment schedule, not a complete statement of the loan account. It helps illustrate how the balance changes and how payments are allocated under the chosen assumptions. It can also help readers compare a schedule’s shape with a lender’s disclosed figures, provided the inputs and payment timing match.

• Balance over time: A descending curve or line represents principal still owed after each payment.
• Principal paid: The amount of each payment that lowers the principal balance.
• Interest paid: The financing charge allocated to each period under the modeled rate and balance.
• Cumulative totals: Some graphs show total principal or interest paid from the beginning through a selected month.

A graph based on a fixed APR and regular payments does not predict future changes in a variable-rate loan. Nor does it automatically account for late payments, payment holidays, fees added to the balance, extra principal payments, or a different final payment. Those events can make the actual balance diverge from the illustrated schedule.

Common Misreadings and Input Errors

A common misconception is that an amortization schedule charges the same dollar amount of interest every month. With a fixed rate, the rate may remain constant, but the interest amount generally changes because the outstanding principal changes. Another mistake is to treat the monthly payment as principal alone; the scheduled payment ordinarily covers both interest and principal, while other charges may be billed separately.

• Enter APR as a yearly percentage, such as 8 for 8%, not as 0.08 or 8 in the monthly-rate field.
• Enter the contractual term in years. The formula converts years to months; do not enter 60 for a five-year term.
• Use the amount financed as principal if that is the figure the loan’s payment is based on. A quoted purchase price may not equal the amount financed.
• Expect small differences if a lender uses daily interest, different rounding, irregular payment dates, or a final payment adjustment.
• Do not read total interest as the full cost of borrowing when fees or other charges are excluded.

When an Amortization Graph Is Useful

The graph is useful when a reader wants to see the timing behind a monthly payment. A payment amount alone does not reveal how quickly the balance falls or how much of the early payments goes to interest. A schedule or graph makes those patterns visible and lets readers inspect a particular month rather than relying only on totals.

For a like-for-like comparison of two hypothetical schedules, keep the principal, APR basis, term, payment frequency, and included charges consistent unless the purpose is to examine how one changed input affects the result. Any real rate, fee, or loan balance should come from the lender’s current disclosure or account information; this calculator’s default is only an example.

Frequently Asked Questions

What does a loan amortization graph show?
A loan amortization graph shows how the outstanding balance and, often, the principal and interest portions of payments change over the repayment term.

Why does the interest portion usually fall over time?
For a fixed-rate loan, periodic interest is calculated on the remaining balance. As principal is repaid, that balance falls, so the interest amount generally falls too.

Does an amortization graph include taxes and insurance?
Not necessarily. A basic loan graph usually models principal and interest only. Taxes, insurance, escrow, and fees must be checked separately unless the calculator explicitly includes them.

Why does my lender’s schedule differ from this estimate?
Differences can result from the actual APR, financed amount, payment dates, daily versus monthly interest calculations, rounding, fees, or a variable rate. Compare the calculator assumptions with the lender’s disclosed terms.

Does an extra payment change the graph?
Yes, if it is applied to principal, an extra payment can reduce the balance faster and change later interest. This calculator does not model extra payments, so its graph would not represent that altered schedule.

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 | $ | round(p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)), 2) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2