The Loan Amortization Formula Explained

The Formula

M = P [ r(1+r)^n ] / [ (1+r)^n - 1 ] where M is the monthly payment, P is the principal, r is the monthly interest rate (annual rate / 12), and n is the number of payments (loan term in months). For a $300,000 mortgage at 6% for 30 years: P = 300,000, r = 0.005, n = 360. This gives M = 300,000 [ 0.005(1.005)^360 ] / [ (1.005)^360 - 1 ] = $1,798.65.

What Each Variable Does

A higher principal (P) increases the payment proportionally. A higher rate (r) increases both the payment and the total interest dramatically. A longer term (n) reduces the payment but increases total interest paid. Doubling the rate from 4% to 8% increases the payment by about 45% but doubles the total interest.