Amortization Schedule by Month: Payment and Interest

An amortization schedule by month shows how each loan payment is divided between interest and principal, and how the balance changes over time. Enter the loan amount, APR, and term to calculate the fixed monthly payment and total interest; the monthly rows can then be built from those figures.

Formula

The calculator uses the standard fixed-payment loan formula. It first converts the annual percentage rate to a monthly rate, then computes the payment that repays principal and interest over the term:

• Monthly rate, r = APR ÷ 1,200, expressed as a decimal per month.
• Number of payments, n = loan term in years × 12.
• Monthly payment, M = round(P × r ÷ [1 − (1 + r)⁻ⁿ], 2).
• Total interest, I = M × n − P.

P is the starting loan principal in dollars, APR is the annual percentage rate in percent, r is the monthly rate, n is the number of monthly payments, and M is the monthly payment in dollars. The payment is rounded to cents before total interest is calculated, so the result uses the displayed payment.

Worked Example

Using the calculator’s defaults: P = $20,000, APR = 8%, and a five-year term:

1. Convert the APR to a monthly rate: r = 8 ÷ 1,200 = 0.0066667, or about 0.66667% per month.
2. Count the payments: n = 5 × 12 = 60.
3. Substitute into the payment formula: M = round[20,000 × 0.0066667 ÷ (1 − (1.0066667)⁻⁶⁰), 2] = $405.53 per month.
4. Calculate total interest using the rounded payment: I = $405.53 × 60 − $20,000 = $4,331.80.

Assumptions

• The APR and scheduled payment remain fixed throughout the modeled term.
• Payments are monthly, with one payment per period; the schedule assumes payments are made as planned.
• Interest accrues monthly at APR ÷ 12, represented by the monthly rate APR ÷ 1,200 when APR is entered as a percentage.
• The calculation excludes fees, taxes, insurance, PMI, escrow, late charges, and other costs because they are not inputs.

How to Build and Read Monthly Rows

The calculator gives the fixed payment and total interest, not a printed row for every month. To make a month-by-month table, begin with the opening balance and repeat the same three calculations for each payment period:

1. Calculate that month’s interest: opening balance × monthly rate.
2. Calculate principal paid: scheduled payment − interest for the month.
3. Calculate the new balance: opening balance − principal paid. Use that new balance as the next month’s opening balance.

For the example, month 1 interest is $20,000 × 0.0066667, approximately $133.33. Principal is $405.53 − $133.33 = $272.20, leaving an estimated balance of $19,727.80. In month 2, interest is calculated on that lower balance, so slightly less of the payment goes to interest and slightly more goes to principal.

A table usually has columns for payment number or date, opening balance, payment, interest, principal, and ending balance. Early in a conventional amortizing loan, interest takes a larger share because the balance is larger. As principal declines, the interest portion generally falls. The payment itself stays level when the rate and scheduled terms are fixed.

What the Schedule Can and Cannot Show

A schedule is a projection of principal and interest under its stated assumptions. It can help explain how the balance is expected to decline and why the total of payments exceeds the amount borrowed. It is not necessarily the lender’s exact payment calendar: actual calculations may depend on dates, daily interest accrual, payment posting, rounding conventions, or loan-specific terms.

It also does not automatically represent the full amount due each month. A mortgage payment, for example, may include taxes or insurance collected with principal and interest. Those items are outside this calculation, as are fees and optional charges. Check the loan disclosure or servicing statement for the actual amount and schedule.

Common Calculation Problems

• Entering APR as a decimal: Enter 8 for 8%, not 0.08. The formula converts the percentage to a monthly decimal by dividing by 1,200.
• Mixing years and months: The input is years; the formula multiplies by 12 to get the number of payments.
• Expecting every row to match exactly: Rounded interest and principal amounts can create a few cents of difference across a long table. A final payment may need adjustment to clear the remaining balance.
• Assuming extra payments are included: They are not. An extra principal payment changes later balances and interest, so it requires a schedule that models the amount and timing of those payments.
• Treating total interest as total borrowing cost: Total interest excludes fees and other costs. It is not the same as a complete cost-of-credit figure.

Frequently Asked Questions

What does an amortization schedule by month show?
It shows each payment period’s opening balance, scheduled payment, interest, principal reduction, and ending balance. Together, the rows show how the loan is projected to be repaid.

Why does the interest portion decrease over time?
For a fixed-rate amortizing loan, interest is calculated on the remaining balance. As principal is repaid, the balance falls, so the interest calculated for later periods generally falls too.

Does this calculator create a complete monthly table?
No. It calculates the fixed payment and total interest. You can create the rows by applying the monthly interest, principal, and ending-balance steps above, or use a schedule tool that outputs every period.

Why might my lender’s schedule differ by a few cents?
Rounding rules, payment dates, daily versus monthly interest methods, and the treatment of the final payment can change individual row amounts. Use the lender’s disclosure and account records for the contractual figures.

Does the monthly payment include taxes and insurance?
No. This formula calculates principal and interest only. Taxes, insurance, escrow, PMI, and fees are not included unless separately modeled.

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