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Home Affordability, Explained

After reading this you can work out the largest home price your income supports under standard lender debt-ratio rules, and understand why that ceiling is a limit rather than a target.

What the calculator answers

Lenders decide how much they will lend you by looking at two ratios: how much of your income goes to housing, and how much goes to all debt combined. The Home Affordability Calculator runs those rules in reverse. Instead of starting from a house price and checking whether you qualify, it starts from your income and hands back the maximum price the ratios allow.

Here is the hook. Suppose you earn 6000 per month before tax, carry 400 in other monthly debt payments, and have 40000 saved. At a 6.5% rate over 30 years, the standard 28/36 rule caps your housing payment at about 1680 per month. That payment supports a loan near 265700, so with your down payment your ceiling lands around 305700. Every number in that chain is reproducible, and the rest of this article shows the arithmetic.

When to use it, and when not to

Use this calculator early, before you tour houses or talk to an agent. It gives you a realistic price band so you look at homes a lender would actually finance. It is also useful for testing "what if" questions: what a higher rate does to your ceiling, or how much a larger down payment buys you.

Do not treat the output as the price you should pay. The ratios describe what a lender will tolerate, not what leaves you comfortable. The calculator also ignores property tax, home insurance, and HOA fees, which many lenders fold into the housing ratio in real life. If those costs are high in your area, your true ceiling is lower than the number shown.

The result is the lender's maximum, not a recommendation. Buying below it leaves room for rate rises, repairs, and changes in income. A payment that fits the ratio exactly can still strain a budget.

The two ratios behind the number

Lenders use two debt-to-income ratios. The front-end ratio (also called the housing ratio) limits your housing payment as a share of gross income. The back-end ratio limits your total debt, housing plus everything else, as a share of gross income.

Front-end ratio
Housing payment divided by gross monthly income. The common ceiling is 28%.
Back-end ratio
All monthly debt payments (housing plus car loans, student loans, credit cards) divided by gross monthly income. The common ceiling is 36%.
Gross income
Income before tax and deductions. Lenders qualify you on gross, not take-home pay.

Each ratio produces its own housing-payment cap. The front-end cap is a fixed slice of income. The back-end cap is a larger slice minus whatever debt you already carry. Your allowed payment is the smaller of the two, because you must satisfy both rules at once.

P_{\text{front}} = \frac{f}{100} \cdot I

Here P_{\text{front}} is the housing payment allowed by the front-end rule, f is the front-end limit in percent (28 by default), and I is gross monthly income.

P_{\text{back}} = \frac{b}{100} \cdot I - D

Here P_{\text{back}} is the housing payment allowed by the back-end rule, b is the back-end limit in percent (36 by default), and D is your other monthly debt. The allowed housing payment is P = \min(P_{\text{front}}, P_{\text{back}}).

Turning a payment into a price

Once you know the allowed monthly payment, you convert it into a loan using the standard mortgage formula, solved for the loan balance. A fixed-rate, fully amortizing loan has this relationship between payment and principal:

L = P \cdot \frac{1 - (1 + i)^{-n}}{i}

Here L is the loan amount, P is the monthly payment, i is the monthly interest rate (annual rate divided by 12, as a decimal), and n is the number of monthly payments (years times 12). The fraction is the present-value factor of an annuity: it tells you how many dollars of loan each dollar of monthly payment can carry.

The maximum price is then the loan plus the cash you bring:

\text{Price} = L + \text{down}

The down payment matters twice. It adds directly to the price here, and in real transactions a larger down payment can also lower your rate and remove mortgage insurance, which raises the loan you can support. This calculator applies it only as the direct addition.

The annuity factor grows as rates fall. At 6.5% over 30 years, each 1 of monthly payment supports about 158.2 of loan. At 4% it supports about 209.5. Same payment, much larger loan.

Reproducing the demo numbers

Use the default inputs: income 6000, debts 400, down payment 40000, rate 6.5%, term 30 years, front-end limit 28%, back-end limit 36%.

  1. Front-end cap: 0.28 \times 6000 = 1680 per month.
  2. Back-end cap: 0.36 \times 6000 - 400 = 2160 - 400 = 1760 per month.
  3. Allowed payment is the smaller of the two: \min(1680, 1760) = 1680. The front-end rule binds here.
  4. Monthly rate: i = 0.065 / 12 = 0.0054167. Payments: n = 30 \times 12 = 360.
  5. Annuity factor: \frac{1 - (1.0054167)^{-360}}{0.0054167} \approx 158.2.
  6. Loan: 1680 \times 158.2 \approx 265700.
  7. Maximum price: 265700 + 40000 = 305700.

The tool rounds slightly differently at intermediate steps, so expect the displayed price to sit within a few hundred of 305700.

How the ceiling moves with the interest rate

Rate is the single input that swings the answer the most, because it reshapes the annuity factor. Your allowed payment stays fixed at 1680, but the loan that payment supports shrinks fast as rates climb.

The ceiling falls as rates rise. At 3% the same payment supports a price near 438000; at 10% it drops below 234000. The marker sits at the 6.5% default.

The lesson is that affordability is mostly a story about rates, not just income. A borrower who qualified for a price in a low-rate year would qualify for far less on the same salary once rates double.

With income 6000, debts 400, down 40000, rate 6.5% and a 30-year term, the front-end cap of 1680 binds and the maximum price is about 305700. Lowering the rate to 4% raises it to about 392900; raising debts to 900 makes the back-end cap of 1260 bind and drops the price to about 239100.

Reading and interpreting the result

Notice which ratio bound your answer. In the demo the front-end cap (1680) was lower than the back-end cap (1760), so paying down other debt would not raise your ceiling. If instead your debts were 900, the back-end cap becomes 0.36 \times 6000 - 900 = 1260, which now binds. In that case every 100 of debt you clear frees 100 of housing payment, lifting the loan by about 100 \times 158.2 = 15820.

Treat the price as a band, not a point. Run it at your current rate and at a rate one point higher. Run it with the payment you would actually be comfortable making, which is often well below the cap. The gap between the lender's ceiling and your comfort level is your safety margin.

Common mistakes

  • Using net income. Lenders qualify on gross income. Entering take-home pay understates your ceiling, but qualifying on gross and budgeting on gross is a trap in the other direction: your actual cash flow is smaller.
  • Forgetting taxes and insurance. Real lenders count property tax, home insurance, and sometimes HOA and mortgage insurance inside the housing ratio. If those add 400 per month, your available principal-and-interest budget drops from 1680 to 1280, cutting the loan by about 400 \times 158.2 = 63280.
  • Leaving out debts that start soon. A car loan you plan to take on counts against the back-end ratio.
  • Assuming the maximum is safe. A payment at exactly 28% of gross income leaves little slack for a rate reset or a lost bonus.

Related tools

Once you have a price band, other calculators refine the picture. Use the Mortgage Calculator to see the full payment and amortization for a specific price. The Down Payment & LTV Calculator shows how your cash changes the loan-to-value and loan amount. Compare buying against renting with the Rent vs Buy Calculator, and if you are still renting, the Rent Affordability Calculator applies the same ratio logic to rent. To plan paying the loan down faster, see the Mortgage Extra Payment Calculator and the Biweekly Mortgage Calculator.

Frequently asked questions

Why does the calculator use gross income instead of take-home pay?

Lenders standardized on gross income because it is easy to verify from tax documents and does not vary with each person's tax situation. The 28% and 36% limits were calibrated against gross figures. Budget on your take-home pay separately, since that is the money that actually reaches your account.

What are the 28 and 36 numbers, and can I change them?

They are the classic conforming-loan ratio limits: 28% of gross income for housing, 36% for all debt. Many loan programs allow higher limits, sometimes 31/43 or more with strong credit. The calculator lets you set both so you can model whatever a lender offers you.

Does a bigger down payment always raise my maximum price?

In this calculator, yes, one to one: the down payment adds directly to the price. In practice it can help more, because a lower loan-to-value ratio may earn a lower rate and remove mortgage insurance, both of which raise the loan you can support.

Why did paying off debt not change my ceiling?

Because the front-end ratio was binding. Debt only affects the back-end cap. If the front-end cap is already the smaller of the two, clearing debt has no effect until it drops enough to make the back-end cap the higher of the two.

Is this the same as loan pre-approval?

No. Pre-approval is a lender's conditional commitment based on your credit, verified income, and their own overlays. This calculator is an educational estimate of the ratio math and does not account for credit score, reserves, or program-specific rules.

This is an educational estimate, not financial advice. Talk to a qualified adviser or mortgage professional before making money decisions.

Try it yourself in the tool

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