Mortgage Amortization Math, Explained with Code

Every mortgage calculator hides the same elegant math: the amortization formula. Here's the full breakdown with JavaScript.

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The core formula

function monthlyPayment(principal, annualRate, years) { const r = annualRate / 12; const n = years * 12; if (r === 0) return principal / n; const factor = Math.pow(1 + r, n); return principal * (r * factor) / (factor - 1); } // $400,000 loan, 6.5% APR, 30 years → $2,528.27/mo

Amortization schedule

function amortizationSchedule(principal, annualRate, years) { const r = annualRate / 12; const payment = monthlyPayment(principal, annualRate, years); let balance = principal; const schedule = []; for (let month = 1; month <= years * 12; month++) { const interest = balance * r; const principalPaid = payment - interest; balance -= principalPaid; schedule.push({ month, interest: +interest.toFixed(2), principal: +principalPaid.toFixed(2), balance: +Math.max(balance, 0).toFixed(2) }); if (balance <= 0) break; } return schedule; }

Extra payments

function payoffWithExtra(principal, annualRate, years, extraMonthly) { const r = annualRate / 12; const basePayment = monthlyPayment(principal, annualRate, years); let balance = principal, months = 0, totalInterest = 0; while (balance > 0) { const interest = balance * r; totalInterest += interest; balance -= (basePayment + extraMonthly - interest); months++; } return { years: (months / 12).toFixed(1), totalInterest: +totalInterest.toFixed(2) }; }