Mortgage Loan Income Calculator

The calculation runs in two stages, and only the second is a mortgage formula.

Stage one — how much payment the income supports. Two ratios are used, both on gross monthly income $I$:

$\text{front-end} = \frac{\text{PITI}}{I}, \qquad \text{back-end} = \frac{\text{PITI} + \text{other debt}}{I}$

PITI is principal, interest, taxes and insurance, plus HOA dues and mortgage insurance where they apply. Pick a ratio $\alpha$ and the housing budget is $\text{PITI} = \alpha I$; under a back-end limit $\beta$ it is $\beta I - \text{other debt}$. The smaller of the two governs.

Stage two — how much loan that payment buys. Strip the non-loan parts to leave principal and interest, then invert the payment formula:

$L = M\cdot\frac{1 - (1+r)^{-n}}{r}$

with $r$ the monthly rate and $n$ the number of payments.

Which ratios a lender applies, what counts as qualifying income, and how taxes and insurance are estimated all vary by lender, loan programme and jurisdiction, and they change. Enter the ratio and rate that apply to you — this page is a calculator, not a lending decision.

Once $L$ is known, the price follows from the down payment fraction $d$:

$\text{Price} = \frac{L}{1 - d}$

A \257{,}884$loan with$20%$down supports a price of$257{,}884/0.80 \approx $322{,}355$.

Working the other way

Given a target payment, the income required at ratio $\alpha$ is

$I = \frac{\text{PITI}}{\alpha}$

and the annual figure is $12I$. This is the more useful direction when you already know the house.

Why property tax matters so much

PITI is the constrained quantity, but only the P&I part buys loan. Every dollar of monthly tax, insurance, HOA or mortgage insurance reduces $M$ one-for-one, and each dollar of $M$ is worth roughly $\dfrac{1 - (1+r)^{-n}}{r}$ dollars of loan — about \158$per dollar at$6.5%$over 30 years. A$$100$swing in the monthly tax estimate moves the affordable loan by roughly$$15{,}800$.

Property tax rates, insurance costs and programme rules are local and change annually. Use your own figures.

• Applying the ratio to net pay: the ratios are conventionally computed on gross income. Using take-home pay understates the result substantially.
• Comparing the ratio against principal and interest only: the front-end ratio is measured on full PITI. Leaving taxes and insurance out inflates the affordable loan.
• Ignoring the back-end constraint: with meaningful car or student debt, the back-end limit almost always binds first — it did in the example below.
• Forgetting to invert the payment formula: $L = M\left(1 - (1+r)^{-n}\right)/r$, not $M \times n$. Multiplying the payment by the number of months counts the interest as principal.
• Confusing the loan with the price: they differ by the down payment, and closing costs sit outside both.
• Treating a computed figure as an approval: underwriting weighs credit, reserves, employment history and programme rules that no formula sees.