Mortgage Affordability Calculator

Start from the monthly payment you can comfortably afford and work backwards to the maximum loan.

Formulas:

Maximum loan: PV = PMT × (1 − (1 + r)⁻ⁿ) / r where r = annualRate / 12, n = years × 12.
Total home price: PV + downPayment. Total interest: PMT × n − PV.

How affordability works

From payment to price, in one inversion

A mortgage payment formula maps a loan to a payment; affordability simply runs it backwards. Take the payment you can live with — say $1,500 — and ask what loan it can service: at 6.5% over 30 years that is $237,316.23. Your down payment then sets the shopping budget: $60,000 down means homes around $297,316.23. Every extra dollar of payment or down payment flows straight into the price you can offer.

The term is a lever, not a detail

Stretching the term lowers the rate at which the balance burns off, so the same payment supports a bigger loan. The chart above makes the trade visible: at $1,500 and 6.5%, 15 years borrows $172,194.62 while 30 years borrows $237,316.23 — $65,121.61 more house. But the longer term pays $302,683.77 of interest against $97,805.38: more than three times the cost for roughly 38% more loan. Pick the shortest term whose payment you can genuinely sustain.

What this deliberately leaves out

The calculator models principal and interest only — the pure loan math. Property taxes, homeowner's insurance, HOA dues, and mortgage insurance sit outside it, and lenders layer their own caps on top (debt-to-income limits, the appraised value, the loan-to-value bracket). Treat the result as your loan envelope, then subtract the extras to get a realistic target price.

The exact simulation behind the numbers

For each month the payment first covers interest on the remaining balance (r = annual rate ÷ 12) and retires the rest as principal. The maximum loan is the starting balance for which the final payment exactly zeroes the balance in month n — the closed form PMT × (1 − (1 + r)⁻ⁿ) / r, evaluated directly with no iteration.

Affordability in Excel and on a TI-84

Work backwards from a payment to a loan with PV functions:

Excel Maximum Loan: =PV(6.5%/12, 360, -1500) returns $237,316.23 — the 30-year loan a $1,500 payment services at 6.5%.
Excel Term Comparison: =PV(6.5%/12, 180, -1500) returns $172,194.62 for 15 years; subtract from the 30-year figure to see the $65,121.61 of extra borrowing a longer term buys.
TI-84 TVM Solver Steps:
1. Press APPS, choose 1:Finance…, and select 1:TVM Solver….
2. Enter I% = 6.5, PMT = -1500, FV = 0, N = 360, P/Y = 12, C/Y = 12.
3. Place the cursor on PV and press ALPHA then ENTER (SOLVE) to calculate 237,316.23.
Sanity Check: feed the solved PV back into =PMT(6.5%/12, 360, -237316.23) — it returns $1,500.00, closing the loop.

Worked examples

Example 1: $1,500/month at 6.5% for 30 years, $60,000 down

Enter monthlyPayment = 1500, annualRate = 6.5, years = 30, downPayment = 60000. Maximum loan: $237,316.23; total home price: $297,316.23. Over the term you pay $540,000.00 total, of which $302,683.77 is interest.

Example 2: Same payment on a 15-year term

Keep the payment and rate, set years = 15. The loan shrinks to $172,194.62 (total price $232,194.62 with the same $60,000 down), but interest falls to $97,805.38 — you keep $204,878.39 versus the 30-year schedule and own the home in half the time.

Example 3: Rate shopping, same budget

Keep monthlyPayment = 1500 and years = 30 but set annualRate = 5.5: the maximum loan rises to $264,182.64 from $237,316.23 at 6.5% — a one-point rate move is worth $26,866.41 of borrowing power at this budget. Rates change what the same payment buys.

Related tools

The Affordability Calculator answers "how much can I borrow?". Related questions:

"What's the payment on a specific loan?" — the Loan / Mortgage Calculator runs the forward direction with a full schedule.
"Which repayment structure should I pick?" — the Fixed-Principal Loan Calculator compares straight-line and fixed-payment amortization.
"How do I save the down payment faster?" — the Savings Goal Calculator turns the down payment into a monthly deposit plan.

Frequently asked questions

How much house can I afford with a $1,500 monthly payment?

At 6.5% over 30 years, $1,500 per month services a maximum loan of $237,316.23. With a $60,000 down payment, that is a home around $297,316.23 — principal and interest only, before taxes and insurance.

How is the maximum loan calculated?

As the present value of the payment stream: maxLoan = PMT × (1 − (1 + r)⁻ⁿ) / r. It is the standard payment formula inverted — the same first step a lender's calculator makes before applying its own caps.

What share of income should the payment be?

The classic 28/36 rule: housing under 28% of gross monthly income, total debt under 36%. A $1,500 payment implies at least about $5,400 of gross monthly income under the 28% rule, more if you carry other debts. Lenders apply their own DTI limits on top of any rule of thumb.

Does a bigger down payment change the maximum loan?

No — the payment, rate, and term fix the loan size. The down payment raises the price you can target: $20,000 down shops $257,316.23, $60,000 down shops $297,316.23, on the same $237,316.23 maximum loan. A larger down payment can also improve your rate and remove mortgage insurance.

15-year or 30-year term?

At 6.5% with $1,500/month, 30 years borrows $237,316.23 at $302,683.77 of interest while 15 years borrows $172,194.62 at $97,805.38. The 30-year maximizes how much house you can buy; the 15-year minimizes what it costs.

Does this include taxes, insurance, or PMI?

No — this models principal and interest only. Taxes, insurance, HOA fees, and mortgage insurance consume real budget; many buyers target a payment 10-20% below their ceiling to leave room for them.