How to Calculate How Much Loan You Can Afford

What loan affordability is

Loan affordability is the biggest loan your monthly payment can support — not the biggest price you can dream of. Lenders work it out from your gross monthly income and the debts you already pay, using a debt-to-income target: the share of your income all your debts together may take. On the worked example here — $7,500.00 a month, $400.00 of debts, a 36% target, 6.5% APR, 30 years, $40,000.00 down — the max loan is $363,884.88 and the max price is $403,884.88. Every figure here is checked against the loan affordability calculator.

The loan affordability formula

Max total monthly debt payment = gross monthly income × DTI target. Max new loan payment = max total − existing monthly debts. Annuity factor F = (1 − (1 + r)⁻ⁿ) / r, where r = APR ÷ 12 and n = the term in months. Max loan = max payment × F. Max price = max loan + down payment. The DTI target is a percent — 36% is 0.36 — and the APR is annual, so 6.5% is 0.065 a year and 0.00541667 a month.

Step 1: Write down the income, debts, and target

Write down the three numbers the formula needs. The gross monthly income is your pay before tax, per month — $7,500.00 on the worked example. The existing monthly debts are what you already pay each month — $400.00 here. The DTI target is the ceiling you are sizing to — 36% here, the common conventional ceiling; 43% is the common FHA ceiling.

Step 2: Multiply the income by the DTI target

Multiply the income by the DTI target for the max total monthly debt payment. On the worked example that is $7,500.00 × 36% = $2,700.00. This is the most all your debts together may take each month — the new loan plus everything you already owe.

Step 3: Subtract the debts for the max payment

Subtract the existing monthly debts from the max total for the max new loan payment. On the worked example that is $2,700.00 − $400.00 = $2,300.00. If the debts eat the whole total, the payment is $0.00 — there is nothing left to borrow with. With $0 of debts, the whole $2,700.00 is yours.

Step 4: Work out the annuity factor and the max loan

Work out the annuity factor, then multiply the payment by it. The monthly rate is 6.5% ÷ 12 = 0.541667%, and the term is 30 years = 360 months, so the factor is (1 − (1 + 0.00541667)⁻³⁶⁰) / 0.00541667 = 158.2108. The max loan is $2,300.00 × 158.2108 = $363,884.88. The factor is why the rate and the term matter so much: at 5.0% it is 186.2816 and the max loan is $428,447.72, and over 15 years it is 114.7964 and the max loan is $264,031.75.

Step 5: Add the down payment for the max price

Add the down payment to the max loan for the max price. On the worked example that is $363,884.88 + $40,000.00 = $403,884.88. The down payment moves the price, not the loan: with $0 down the max loan is still $363,884.88 and the max price is $363,884.88.

Step 6: Reverse it when you need a target

Reverse it when you need a target. The income for a $3,000.00 max payment is $9,444.44 — the exact income is 9444.4444, and at $9,444.44 the payment is $3,000.00 exactly. The DTI for a $2,500.00 payment is 38.67%: at 38.67% the payment is $2,500.25, $0.25 over the target, because the DTI is rounded. The APR for a $400,000.00 max loan is 5.61%: at 5.61% the loan is $400,202.04. And 34 years is the first whole number of years at which the max loan reaches $375,000: at 34 years the max loan is $377,756.17, while 33 years gives $374,617.92.

Worked example

Put the six steps together for $7,500.00 a month, $400.00 of debts, 36% DTI, 6.5% APR, 30 years, $40,000.00 down. The max total is $7,500.00 × 36% = $2,700.00. The max payment is $2,700.00 − $400.00 = $2,300.00. The factor is 158.2108. The max loan is $2,300.00 × 158.2108 = $363,884.88. The max price is $363,884.88 + $40,000.00 = $403,884.88. A $10,000.00-a-month income lifts the max loan to $506,274.62, and $0 of debts lifts it to $427,169.21.

How the numbers change

A rate of 5.0% lifts the max loan to $428,447.72 and the max price to $468,447.72. A 43% DTI lifts the max loan to $446,945.57 and the max price to $486,945.57. A term of 15 years cuts the max loan to $264,031.75 and the max price to $304,031.75. An income of $5,000.00 a month with $800.00 of debts gives a $1,800.00 total, a $1,000.00 payment, a $158,210.82 max loan, and a $198,210.82 max price.

Working backwards

It also runs in reverse. The debts for a $2,000.00 max payment are $700.00: at $700.00 the payment is $2,000.00 exactly. The down payment for a $450,000.00 max price is $86,115.12: at $86,115.12 the price is $450,000.00 exactly. The income for a $3,000.00 payment is $9,444.44, and the DTI for a $2,500.00 payment is 38.67%.

What the calculation leaves out

Four things are left out. First, this is a sizing rule, not an approval — lenders also check credit score, employment history, and reserves. Second, it does not model the front-end (housing-only) ratio, which is a separate ceiling. Third, it does not add property taxes, homeowner’s insurance, HOA dues, or PMI to the payment. Fourth, it assumes a fixed rate and the same payment every month, and it does not model closing costs or a rate that changes part-way through. For the payment on a loan you already have in mind, see the loan calculator, and for your DTI ratio alone, see the debt-to-income ratio calculator.

What to do next

Run your own numbers through the loan affordability calculator — and if the payment it gives is more than you are comfortable paying each month, size the loan to the payment you can live with, not the ceiling.