Amortization Table Formula: Calculate Each Payment

An amortization table shows how each loan payment is divided between interest and principal, and how the remaining balance changes over time. Enter the loan amount, annual APR, and term below to calculate the fixed monthly payment and total interest; the formula for each row of the table follows.

Formula

For a fixed-rate loan with equal monthly payments, calculate the payment using:

PMT = P × r / [1 − (1 + r)⁻ⁿ]

• PMT is the monthly payment, in dollars.
• P is the starting principal, or loan amount, in dollars.
• r is the monthly interest rate as a decimal: annual APR divided by 12 and then by 100 (APR ÷ 1,200).
• n is the total number of monthly payments: loan term in years × 12.

The calculator applies this formula to the stated inputs and displays the payment to the nearest cent. Total interest is calculated as the displayed monthly payment multiplied by the number of payments, minus the original principal. An amortization table uses the payment to calculate each period’s interest and principal portions.

Worked Example

Using the calculator’s defaults: principal P = $20,000, APR = 8%, and term = 5 years.

1. Convert APR to a monthly decimal rate: r = 8 ÷ 1,200 = 0.0066666667.
2. Find the number of payments: n = 5 × 12 = 60.
3. Substitute into the payment formula: PMT = 20,000 × 0.0066666667 ÷ [1 − (1 + 0.0066666667)⁻⁶⁰].
4. The unrounded result is about $405.5279, 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 stays fixed for the full term.
• Payments are equal, made monthly, and paid at the end of each monthly period.
• Interest accrues monthly at APR ÷ 12, with no separate daily-interest or compounding adjustment.
• Fees, taxes, insurance, PMI, escrow, late payments, and extra principal payments are not included.

How an Amortization Table Works

Each row represents one payment period. To build a row, multiply the balance at the start of the month by the monthly rate to find that month’s interest. Subtract this interest from the scheduled payment to find the principal reduction. Subtract that reduction from the opening balance to get the next month’s balance.

For the example, the first month’s interest is $20,000 × 0.0066666667, or about $133.33. Of the $405.53 payment, about $272.20 therefore reduces principal, leaving an estimated balance of $19,727.80. Later, the interest portion generally falls as the balance declines, while more of each fixed payment goes toward principal.

The balance after k payments can also be calculated directly, before considering rounding adjustments: B_k = P(1 + r)^k − PMT × [(1 + r)^k − 1] ÷ r. Here, B_k is the balance after k payments; P, r, and PMT have the meanings above, and k is the number of payments already made. A row-by-row schedule may differ slightly from this compact balance formula because actual statements round interest and payments to cents each period.

How to Read the Results

The monthly payment is the scheduled amount under the formula’s assumptions; it is not necessarily the complete amount due on a bill. For a mortgage or another loan with separately billed charges, the amount collected may include items the calculation does not model. Total interest is the sum implied by the regular payment schedule, not the total cost of borrowing including every possible charge.

At the start of a fully amortizing loan, interest takes a larger share of each payment because the outstanding balance is largest. Principal reduction accumulates over time, and the final scheduled payment brings the balance to approximately zero. A lender’s servicing system may adjust the final payment by a small amount to account for payment-date conventions and rounding.

Common Mistakes and Limits

• Entering APR as a decimal: Enter 8 for 8%, not 0.08. The formula divides the percentage by 1,200 to obtain a monthly decimal rate.
• Mixing years and months: This calculator accepts years and converts the term to months. If another formula expects months, use years × 12.
• Assuming the first payment is all principal: Interest for a period is calculated before the payment reduces the balance.
• Ignoring rounding: A displayed payment rounded to cents may cause the schedule’s last balance or total to vary slightly from calculations that keep many decimal places throughout.
• Treating every loan as fixed-rate and fully amortizing: Variable rates, interest-only periods, balloon payments, irregular payment dates, and skipped or extra payments require a different schedule or additional inputs.

The formula also assumes that the full stated principal is borrowed and that regular payments occur as scheduled. If a lender quotes a different payment, check whether the quoted amount includes fees, a different compounding convention, a different first-payment date, or other terms not represented here. Obtain the actual APR and payment details from the lender rather than treating the example inputs as market figures.

Frequently Asked Questions

What is the formula for an amortization table?
First calculate the fixed payment with PMT = P × r ÷ [1 − (1 + r)⁻ⁿ]. For each period, interest equals the opening balance times r; principal equals payment minus interest; and the closing balance equals opening balance minus principal.

How do I calculate the interest in each row?
Multiply the balance at the start of that period by the monthly rate. For example, at an 8% APR under monthly compounding, the monthly rate is 8 ÷ 1,200, or about 0.0066667.

Does an amortization payment include taxes and insurance?
Not in this calculation. It estimates principal and interest only; taxes, insurance, escrow, PMI, fees, or other charges require separate amounts and may affect a bill.

Why does the schedule show slightly different totals?
Schedules may round each month’s interest to cents, while a formula may retain more precision until the end. Payment dates, the first period’s length, and final-payment adjustments can also change the exact figures.

Can I use this formula for an adjustable-rate loan?
It can calculate a payment for a period when the rate is known and held constant, but it does not model future rate changes. A new payment calculation may be needed when the rate resets.

Using the Estimate

Use the schedule to see how a fixed payment is allocated over time, compare the effect of different hypothetical amounts or terms, or check the arithmetic behind a quoted principal-and-interest payment. It does not determine eligibility or account for the complete terms of a loan. 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