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Money & Finance

How Loan Amortization Works

See how a fixed-rate loan payment splits into interest and principal each month, why early payments are interest-heavy, and how to read an amortization schedule.

Understanding the Calculation

A fixed-rate installment loan (mortgage, auto loan, personal loan) is repaid with equal periodic payments over a set term. The size of that payment is calculated so that the loan reaches exactly zero balance at the end of the term.

Every payment is split into two parts: the interest owed on the current balance, and principal, which reduces the balance. Interest is recalculated each period based on the balance remaining at that point — not on the original loan amount.

Because the balance is largest at the beginning of the loan, the interest portion of each payment is largest at the beginning too. As the balance shrinks, less of each payment goes to interest and more goes to principal, even though the total payment stays flat.

The Formula

Fixed-Rate Loan Payment Formula
M = P * [r * (1+r)^n] / [(1+r)^n - 1]

This formula solves for the single fixed payment that fully amortizes the loan — meaning the balance reaches exactly zero after the final scheduled payment, with every payment identical in size.

Variables & Definitions

M— Monthly Payment
The fixed amount paid each period for the life of the loan.
P— Principal
The original loan amount borrowed.
r— Periodic Interest Rate
The annual interest rate divided by the number of payments per year (annual rate / 12 for monthly payments).
n— Number of Payments
Total number of payments over the loan term (loan term in years * 12 for monthly payments).

Worked Example

Worked Example: $300,000 Loan at 6% Over 30 Years

A $300,000 loan at a 6% annual interest rate, repaid monthly over a 30-year (360-payment) term.

Starting Inputs
  • Loan Amount:$300,000
  • Annual Rate:6%
  • Term:30 years (360 monthly payments)
Step-by-Step Calculation
  1. 1

    Find the periodic rate

    Divide the annual rate by 12: 0.06 / 12 = 0.005.

    r = 0.06 / 12 = 0.005
    Result: 0.5% per month
  2. 2

    Calculate the fixed monthly payment

    Apply the payment formula with P=300000, r=0.005, n=360.

    M = 300000 * [0.005*(1.005)^360] / [(1.005)^360 - 1]
    Result: M ≈ $1,798.65
  3. 3

    Split the first payment into interest and principal

    Interest owed on the starting balance: 300000 * 0.005 = $1,500.00. The remainder of the payment reduces principal.

    $1,798.65 - $1,500.00 = $298.65
    Result: $1,500.00 interest, $298.65 principal
  4. 4

    Estimate total interest paid over the full term

    360 payments of $1,798.65 total roughly $647,514. Subtracting the original $300,000 principal gives the total interest paid over the life of the loan.

    (1798.65 * 360) - 300000 ≈ $347,514
    Result: ≈ $347,514 total interest
Conclusion: On this loan, the very first payment is about 83% interest and only 17% principal. That ratio flips steadily over the 30-year term as the balance shrinks, even though the $1,798.65 payment amount never changes.

Calculate Your Own Numbers

Put these formulas into practice with our free, in-browser calculators:

Amortization Calculator

Generate a full period-by-period amortization schedule for any fixed-rate loan.

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Loan Calculator

Calculate payment amount, total interest, and payoff timeline for a fixed-rate loan.

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Mortgage Calculator

Estimate a monthly mortgage payment including principal and interest.

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What the Results Mean For You

  • A lower rate or shorter term both reduce total interest paid, but a shorter term raises the monthly payment because the same principal is repaid over fewer payments.
  • Two loans with the same rate and payment size but different terms will have very different total interest costs — the longer the term, the more total interest accrues, because the balance stays higher for longer.
  • An amortization schedule (the period-by-period table of interest, principal, and remaining balance) is the clearest way to see exactly how much of a given payment builds equity versus how much is the cost of borrowing.

Common Pitfalls & Mistakes

Assuming equal payments mean equal progress on the balance

Because the payment amount is fixed but the interest/principal split shifts every period, the loan balance does not decrease by the same amount each month — it decreases slowly at first and faster later.

Using the annual rate instead of the periodic rate in the formula

The rate inside the payment formula must match the payment frequency — for monthly payments, divide the annual rate by 12 first.

Confusing total payments with total interest

Total interest is the sum of all payments minus the original principal, not the payment amount itself or the stated annual rate.

Authoritative References & Sources

All formula representations and regulatory context are verified against authoritative public sources:

  • What Is Amortization?Consumer Financial Protection Bureau (CFPB)

    Federal consumer-finance reference explaining how loan amortization schedules work.

    Visit source documentation