Amortization Schedule Calculation

Purpose

This calculator produces a month-by-month repayment schedule for a fixed-rate loan, showing how each payment splits between interest and principal, how the loan balance declines over time, and the running totals paid. It is useful for anyone planning or reviewing a mortgage, auto loan, or other installment loan who wants to see exactly how the debt is paid off.

Background

How a fixed-rate loan is repaid

A standard amortizing loan charges a fixed Monthly Payment for the entire term. Each payment first covers the interest owed on the Remaining Principal for that month; whatever is left over reduces the principal itself. Early in the loan, most of each payment goes to interest, because the outstanding balance is largest then. As the balance shrinks, less of each payment goes to interest and more goes to principal, even though the payment amount itself never changes.

Inputs

Loan Amount

The total amount borrowed at the start of the loan.

Annual Interest Rate

The loan's nominal annual interest rate, entered as a percentage (for example, 5.0 for 5%). It is converted internally to a monthly rate by dividing by 12.

Loan Term Years

The number of years over which the loan is repaid. Together with 12 monthly payments per year, this determines the total number of payments.

Results

Amortization Schedule

A table with one row per monthly payment, from Payment Number 1 through the total number of payments (Loan Term Years × 12):

Payment Number — the sequence number of the payment.
Monthly Payment — the fixed amount paid every month; it is the same on every row.
Principal Payment — the portion of that month's payment that reduces the loan balance.
Interest Payment — the portion of that month's payment that covers interest on the remaining balance; it shrinks from row to row as the balance declines.
Total Principal — the cumulative principal paid from Payment 1 through this row.
Total Interest — the cumulative interest paid from Payment 1 through this row.
Total Payment — Total Principal plus Total Interest, the cumulative amount paid so far.
Remaining Principal — the loan balance still owed after this payment; it reaches (approximately) zero on the final row.

Amortization Chart

A line chart plotting Total Principal, Total Interest, Total Payment, and Remaining Principal against the payment number, so you can see at a glance how cumulative payments grow and the balance declines over the life of the loan.

Understanding the Calculation

The monthly interest rate is the Annual Interest Rate divided by 12 (and by 100 to convert from a percentage). The number of payments is Loan Term Years × 12. The fixed Monthly Payment is calculated with the standard amortization formula so that exactly this many equal payments pay off the Loan Amount in full, including all interest:

$\text{Monthly Payment} = \dfrac{\text{Loan Amount} \times r}{1 - (1+r)^{-n}}$

where $r$ is the monthly interest rate and $n$ is the number of payments.

For each payment, in order: Interest Payment = Remaining Principal × monthly rate; Principal Payment = Monthly Payment − Interest Payment; Remaining Principal is then reduced by that Principal Payment before moving to the next row.

Example

Using the default inputs — a Loan Amount of 100,000, an Annual Interest Rate of 5.0%, and a Loan Term of 10 years (120 monthly payments) — the calculator finds a fixed Monthly Payment of 1,060.66 for every payment. The schedule shows, for example:

Payment 1: Interest Payment 416.67, Principal Payment 643.99, Remaining Principal 99,356.01.
Payment 3: Total Interest 1,241.94, Total Principal 1,940.03, Remaining Principal 98,059.97.
Payment 120 (the final payment): Principal Payment 1,056.25, Interest Payment 4.40, Total Principal 100,000.00, Total Interest 27,278.62, Total Payment 127,278.62, Remaining Principal effectively 0.

This shows that over the life of the loan, total interest paid (27,278.62) adds about 27% on top of the original 100,000 borrowed, and that the split between principal and interest shifts steadily toward principal as the balance is paid down.

Important Assumptions and Interpretation

The loan is assumed to be fixed-rate, with equal monthly payments and no extra payments, fees, insurance, or taxes included.
Interest is assumed to compound and accrue monthly on the remaining principal only, using the annual rate divided evenly by 12.
Rounding to two decimal places in the schedule and chart values means the very last row's Remaining Principal may show as a small residual (for example, -0.00) rather than exactly zero.
Results assume the interest rate and payment amount stay constant for the entire term; they do not reflect adjustable-rate loans, refinancing, or prepayments.