What the formula calculates
The monthly loan payment M on a fixed-rate loan is calculated from the principal P, the monthly interest rate r (annual rate divided by 12), and the number of payments n (loan term in months). The formula M = P[r(1+r)^n] / [(1+r)^n - 1] distributes payments so that equal monthly amounts cover both interest and principal retirement over the full term.
Breaking down a payment
In the early months of a loan, most of each payment covers interest. As the principal reduces, the interest portion shrinks and the principal portion grows. This is called amortization. By the final payment, nearly the entire amount goes to principal. An amortization schedule shows this breakdown for every payment over the loan term.
Worked example
A $250,000 mortgage at 6.5% annual interest over 30 years (360 months). Monthly rate r = 0.065/12 = 0.005417. M = 250000 × [0.005417 × (1.005417)^360] / [(1.005417)^360 - 1] ≈ $1,580. Total paid over 30 years: $568,800. Total interest: $318,800.
Effect of extra payments
Adding extra to the principal each month dramatically reduces total interest paid and shortens the loan term. On the example above, an extra $200 per month reduces the loan term by approximately 5 years and saves around $60,000 in interest.