Mortgage Affordability Calculator

Max housing payment = min(front-end % × income, back-end % × income − existing debts). Strip out escrow (taxes, insurance, PMI, HOA) to get the affordable principal & interest, then invert the loan formula: loan = P&I ÷ [ r(1+r)ⁿ ⁄ ((1+r)ⁿ − 1) ]. Max home price = max loan + down payment.

How a lender decides what you can borrow

Affordability is not really about the house — it is about your income and your debts. Lenders apply two debt-to-income (DTI) limits. The front-end ratio caps your housing payment alone at a share of gross income (the classic figure is 28%). The back-end ratio caps your housing payment plus every other monthly debt — car loans, student loans, credit-card minimums — at a larger share (typically 36%). Your maximum housing payment is whichever of those two limits is lower, and this calculator works it out, then turns it into the largest loan and home price that fit.

The key move is that the calculator runs the maths backwards. Instead of starting with a house price, it starts with the payment you can afford, strips out the escrow costs that share that payment, and inverts the loan formula to find the principal that produces it. Add your down payment and you have the maximum home price.

Worked example — $120,000 income, $500 of existing debts, 6.5% over 30 years, $60,000 down: Front-end cap: 28% × $10,000/mo = $2,800. Back-end cap: 36% × $10,000 − $500 = $3,100. The front-end limit binds, so the housing budget is $2,800. Taxes and insurance take about $534 of that, leaving roughly $2,266 for principal and interest — which supports about a $359,000 loan, or a $419,000 home with the down payment.

Which limit binds — and why debts matter so much

The calculator tells you which cap is binding, and it is worth understanding the difference. If the front-end limit binds, your housing budget is set purely by income — paying down debts will not raise it. If the back-end limit binds, your existing debts are the brake: every dollar of monthly debt payment directly reduces the housing payment a lender will allow, and clearing a car loan or a card balance can lift your budget substantially. The two DTI figures shown at the maximum let you see how much headroom each ratio has.

Both caps are adjustable here. The 28/36 guideline is conventional, but many loan programmes stretch the back-end ratio to 43% or even higher, so you can model a specific lender’s limits. Be careful, though: qualifying for a payment is not the same as comfortably affording it.

Escrow, rates and the down payment

A common mistake is to size the loan off the whole housing budget — but taxes, insurance and any PMI or HOA come out of that same payment, leaving less for principal and interest. The calculator subtracts the escrow costs first, so the loan it reports is the real one. Because property tax is usually a percentage of the home’s value and PMI a percentage of the loan, the maths is circular; the calculator solves it exactly, and applies PMI only when the down payment works out below 20%.

Two levers move the answer a lot. The interest rate is one — the sensitivity table and chart show how the maximum loan and price rise and fall as the rate moves, which matters in a changing market. The down payment is the other: it adds directly to the home price you can reach, and a larger one can also push you past the 20% threshold and remove PMI, freeing up budget for a bigger loan.