Mortgage Formula Explained

This reference explains the Mortgage formula used by our free Mortgage Calculator. Use it to understand variables, units, and common mistakes before you calculate.

The formula

PMT = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1] where r = APR/12, n = months

Variables and units

• P — Loan principal (amount borrowed) ($)
• r — Monthly interest rate (APR ÷ 12) (decimal)
• n — Total number of monthly payments (months)

Worked example

Inputs: $300,000 loan, 6.5% APR, 30-year term

1. r = 0.065 / 12 = 0.005417
2. n = 30 × 12 = 360 months
3. PMT = 300,000 × [0.005417 × (1.005417)^360] / [(1.005417)^360 − 1]
4. PMT ≈ $1,896.20 per month

Result: Monthly P&I payment ≈ $1,896 (excluding taxes and insurance)

When to use this formula

Use this formula when you need a quick mortgage estimate with values you already know. Our Mortgage Calculator applies the same relationship automatically so you can verify handwritten work.

Common mistakes

• Forgetting taxes, insurance, and HOA in affordability planning
• Using APR as monthly rate without dividing by 12
• Assuming quoted rates without checking credit score impact

Frequently asked questions