Formula explained

How loan amortization works

Why your early payments are mostly interest, and your last payments are mostly principal — explained without the textbook.

5 min readReviewed May 1, 2026

Quick answer

Each fixed monthly payment is split: interest is charged on the remaining balance, and whatever's left pays down the principal. Early on, the balance is huge, so most of your payment is interest.

The amortization formula

M = P · r ÷ (1 − (1 + r)⁻ⁿ), where P is the loan amount, r is the monthly interest rate, and n is the number of payments.

It's designed to make every monthly payment the same, even though the split between interest and principal shifts month by month.

Inside one month's payment

  1. 1. 1. Interest first

    Multiply the current balance by the monthly rate.

  2. 2. 2. Principal second

    Subtract that interest from the fixed payment — what's left reduces the balance.

  3. 3. 3. Repeat

    Next month's interest is charged on the new, smaller balance.