Loan Calculator

The Loan Payment Formula

Fixed-rate loans are priced with the amortization formula M = P × r(1+r)ⁿ / ((1+r)ⁿ − 1). Here P is the principal, r is the monthly rate (annual rate divided by 12), and n is the number of monthly payments (years × 12). For a $25,000 loan at 5% annual interest over 4 years, r = 0.004167 and n = 48, giving a monthly payment of about $575.73.

How Amortization Works

Every payment is split between interest and principal, but the mix shifts over time. Early on, most of the payment covers interest on a large balance; as the balance falls, more of each fixed payment goes to principal. This is why paying a little extra in the first years has an outsized effect — you are attacking the balance while interest charges are at their highest.

Interest Rate and Term Trade-offs

Two levers control the cost of a loan: the interest rate and the term. A lower rate reduces both the payment and the total interest. A longer term reduces the monthly payment but increases total interest, because you carry the balance longer. Comparing scenarios side by side — say 15 versus 30 years, or 6% versus 7% — reveals how much a small rate change or a shorter term is really worth over the life of the loan.

Using the Results to Plan

Beyond the monthly payment, watch the total cost and total interest figures, since they show what borrowing actually costs you. Use them to check affordability (lenders often prefer housing costs under about 28% of gross income), to weigh refinancing when rates drop, and to test the impact of a larger down payment or extra principal payments. Property taxes, insurance, and lender fees are not part of the base payment formula, so budget for those separately.