What is loan amortization?

Amortization is the process of paying off a loan with fixed payments where each payment covers the interest due plus a portion of principal, so the balance reaches zero at the end of the term.

What is the amortization formula?

M = P × [r(1+r)^n] ÷ [(1+r)^n − 1], where M is the payment, P is principal, r is the monthly rate, and n is the number of payments.

Why do early payments go mostly to interest?

Interest is charged on the remaining balance, which is largest at the start. Early payments cover that large interest charge first, leaving less to reduce principal. Over time the balance shrinks and more of each payment goes to principal.

Loan Amortization Formula Explained

Amortization is the mathematical process that turns a lump-sum loan into a fixed monthly payment. Every installment loan — mortgages, auto loans, personal loans, and EMIs — uses the same underlying formula. Understanding it tells you exactly why your payment is what it is, and how to pay less interest.

The Formula

M = P × [ r(1+r)^n ] ÷ [ (1+r)^n − 1 ]

M = fixed monthly payment
P = principal (amount borrowed)
r = monthly interest rate (annual rate ÷ 12)
n = number of payments (years × 12)

The formula is derived by setting the present value of all future payments equal to the principal. The numerator scales the payment by the interest factor, and the denominator ensures the balance reaches exactly zero after n payments.

Worked Example

Borrow $20,000 at 8% annual interest for 5 years:

P = $20,000
r = 0.08 ÷ 12 = 0.0066667
n = 5 × 12 = 60

The monthly payment works out to roughly $405.53. Over 60 payments you repay $24,331.80, meaning $4,331.80 of pure interest — about 22% of the original loan.

How Each Payment Splits

In month one, interest is $20,000 × 0.0066667 = $133.33, so only $272.20 goes to principal. By month 30, the balance has fallen, and more of the $405 goes to principal. This is the signature of amortization: interest-heavy early, principal-heavy late.

Simple vs. Amortized Interest

Simple interest charges a flat rate on the original principal only. A $20,000 loan at 8% simple for 5 years costs $8,000 in interest.
Amortized interest charges on the declining balance, so the same loan costs only about $4,332 — because you reduce the balance every month.

This is why “8% simple” and “8% amortized” are not the same price. Always ask which one a lender means.

How to Pay Less Interest

Because interest follows the balance, three moves reduce your total cost:

A larger down payment — borrow less to begin with.
A shorter term — a 3-year loan has a higher monthly payment but far less total interest than a 5-year loan.
Extra principal payments — each extra dollar reduces the balance that future interest is charged on.

Run your own numbers with the Loan Calculator and use the extra-payment field to see the savings.