How is mortgage affordability calculated?

The formula, a worked example and the assumptions behind the result. Figures cover principal and interest only and exclude taxes, insurance, PMI and HOA fees.

Can I afford a $350,000 house on a $2,000 monthly budget?

On a 30-year term at 6.5% APR with $40,000 down, a $2,000 monthly payment supports a price of about $356,760, so a $350,000 home is within range before taxes and insurance. Figures are estimates for planning.

Is this mortgage affordability calculator free to use?

Yes. It runs entirely in your browser, needs no account and stores nothing on a server.

Mortgage Affordability Calculator

Two questions, one answer: what can you afford, or what will it cost. Find the monthly payment on a mortgage or the price you can qualify for.

What do you want to find?

Home price ($)

Down payment ($)

Interest rate (APR)

Loan term (years)

Result

The formula

Both questions use the same amortization formula, applied backwards or forwards. The loan balance is paid down in equal monthly instalments over the term, and the rate is the annual rate divided by 12 for a monthly rate.

Monthly payment: loan × [r(1 + r)ⁿ] ÷ [(1 + r)ⁿ − 1], where r is the monthly rate (APR ÷ 12) and n is the number of months (years × 12).
Loan amount from a payment: loan = payment × [((1 + r)ⁿ − 1) ÷ (r(1 + r)ⁿ)]. The affordable price is this loan amount plus your down payment.

Worked examples

Payment on a $350,000 home, 20% down, 6.5% APR, 30 years: loan = 350,000 − 70,000 = 280,000. Monthly rate r = 0.065 ÷ 12 = 0.0054167. n = 30 × 12 = 360. payment = 280,000 × [0.0054167(1.0054167)³⁶⁰] ÷ [(1.0054167)³⁶⁰ − 1] = 280,000 × 0.0063208 = $1,769.83 per month.
Price you can afford on $2,000/month, 6.5% APR, 30 years, $40,000 down: n = 360. (1.0054167)³⁶⁰ = 7.0454. loan = 2,000 × [(7.0454 − 1) ÷ (0.0054167 × 7.0454)] = 2,000 × [6.0454 ÷ 0.038164] = 2,000 × 158.38 = $316,760. price = 316,760 + 40,000 = $356,760.

These figures cover principal and interest only. Property taxes, home insurance, PMI and HOA fees are not included, so the real monthly cost of the home will be higher. They also assume a fixed-rate loan; an adjustable-rate mortgage (ARM) will change your payment after the fixed period.