The formula
Monthly loan payments are calculated using the standard amortization formula: M = P × [r(1+r)^n] / [(1+r)^n − 1], where P is the loan principal (the amount borrowed), r is your monthly interest rate (annual rate divided by 12), and n is the total number of monthly payments (loan term in years × 12).
Step 1: Convert your annual rate to a monthly rate
Take your loan's annual interest rate and divide it by 12. For example, a 6% annual rate becomes a monthly rate of 0.5%, or 0.005 when written as a decimal — this is the number you'll use as r in the formula.
Step 2: Work out your total number of payments
Multiply your loan term in years by 12. A 30-year mortgage has 360 monthly payments; a 5-year car loan has 60.
Step 3: Plug the numbers into the formula
For a $300,000 loan at 6% annual interest over 30 years: r = 0.005, n = 360. Working through the formula gives a monthly payment of $1,798.65 — the same result you'd get from any online loan calculator, since they're all using this identical formula underneath.
Why lenders use this specific formula
This formula guarantees that by your final payment, you'll have paid off the loan exactly — no more, no less — while paying interest only on the remaining balance each month. Early payments are mostly interest since the balance is still high; later payments are mostly principal since the balance has shrunk.
Skip the manual math
If you'd rather not do the calculation by hand, our free loan calculator does this instantly — just enter your loan amount, interest rate, and term to see your monthly payment, total paid, and total interest.