Mortgage affordability calculator and formula

This is the debt-to-income rule run backwards. Instead of asking what ratio a payment produces, it starts from the ratio a lender will accept and asks how large a loan fits inside it.

Enter gross monthly income, the other debt payments a lender will count, the rate and term, the limit your lender works to, what property tax and insurance cost each month, and the cash you have for a deposit. The chain runs income to a total debt budget, to a housing budget, to a principal and interest budget, and finally to the loan that budget supports and the price it buys.

It opens on the inputs of the first worked example below. On $9,000 a month with $650 of other debts and $500 of monthly tax and insurance, a 43 percent total debt limit supports a loan of $430,333.43 over 30 years at 6.5 percent. The 28 percent housing test described in the next section runs alongside it and stops at $319,585.86, and because both tests have to pass, that smaller figure is the one the calculator leads with: a price of $379,585.86 with $60,000 down rather than the $490,333.43 the total debt test on its own would have reached.

Read every one of those figures as a ceiling. The largest loan a rule permits is a different question from the largest loan a person should take, and the two answers are rarely the same number.

United States underwriting applies two debt-to-income tests, and both get called DTI, which is why people quote one and mean the other.

The back-end ratio counts every required monthly payment: the proposed housing payment plus car loans, student loans, card minimums, support orders and anything you co-signed. That is the test this calculator runs from the limit you pick, which is why other debts are an input at all.

The front-end ratio counts housing on its own, as a share of gross pay. A long-standing rule of thumb in the United States pairs a 28 percent front-end test with a 36 percent back-end test. The debt-to-income calculator works both ratios forwards from payments you already have.

Both tests have to pass, so the binding one is whichever gives the smaller answer. The second worked example runs a 28 percent front-end rule against the same $9,000 of income and stops at a loan of $319,585.86, well under the $430,333.43 the back-end test allowed. An applicant with almost no other debt is often capped by the housing test, while an applicant carrying a car loan and student loans is usually capped by the total debt test.

The limits themselves are set by the lender and by the loan program behind the mortgage. They differ between programs, they get revised, and an automated underwriting decision can sit above the number a loan officer quotes you. Use the limit your lender actually applies rather than one copied out of an article.

The pairing moves as well. The 28 and 36 pair belongs together as a rule of thumb, government-backed programs publish their own pair, and some automated underwriting judges the total debt figure on its own without applying a separate housing test at all. The calculator above runs the 28 percent housing test next to whichever total debt limit you pick, which makes it a useful second reading rather than a rule your lender is bound to apply.

A United States mortgage payment is usually quoted as PITI: principal, interest, taxes and insurance. The lender's ratio is applied to the whole of it, and the servicer often collects all four in one bill through an escrow account. Only the first two are the loan.

That is why tax and insurance are subtracted before the loan size is worked out. In the first example, $3,220.00 of housing budget becomes $2,720.00 of principal and interest once $500 of tax and insurance comes out, and it is the $2,720.00 that gets turned into a loan. Every extra dollar of tax or insurance is a dollar of borrowing power gone, at roughly 158 dollars of loan for each dollar of monthly payment on a 30 year loan at 6.5 percent.

Homeowners association dues belong in the same subtraction, and so does mortgage insurance when the deposit is small enough for a lender to require it. Property tax rates vary by state and by county, and insurance premiums vary more between two addresses than most buyers expect, so an escrow figure borrowed from a listing in another county is not a figure to plan with. Get a quote for the actual property.

There is a loop in this worth watching. Tax and insurance scale with the property, but the figure you type is fixed while the answer moves, so a ceiling that lands well above the house whose escrow you quoted is not yet consistent with itself. Enter the escrow for a property near the price the tool returns, then run it again and let the two settle.

The part of the payment that clears the debt rather than paying for the use of the money is the principal, and the way that split moves over the years is how amortisation works.

The budget side of this calculation comes from income and debts. The rate has no effect on it at all. What the rate changes is how much loan a fixed monthly budget buys, and that link is stronger than most buyers expect.

The third worked example moves the rate from 6.5 percent to 7.5 percent and changes nothing else. The same $2,720.00 a month borrows $389,007.95 instead of $430,333.43, about 9.6 percent less. The price ceiling falls by a smaller share, from $490,333.43 to $449,007.95, about 8.4 percent, because the $60,000 of deposit does not shrink when the rate moves. No income was lost and no debt was added. The rate did all of it.

Percentage point, not point. On a mortgage a point already means something else: one point is a fee of one percent of the loan, paid at closing, usually to buy the rate down. A move from 6.5 to 7.5 is a hundred basis points, and it is worth keeping the two senses apart when a lender quotes both to you in the same sentence.

Which rate goes in the box matters as much as its size. The calculation wants the note rate on the loan and divides it by 12, so it is a nominal annual rate quoted with monthly compounding. Two neighbouring numbers are the wrong ones. A Truth in Lending APR, the disclosure figure a United States lender has to show, folds origination fees and mortgage insurance into one annual rate and so sits above the note rate: a quarter of a percentage point of spread, which is ordinary, takes about 2.5 percent off the ceiling. An effective annual rate is wrong in the same direction, because 6.5 percent compounded monthly compounds up to 6.70 percent a year, and entering 6.70 would cut the ceiling by about 2 percent. Neither slip announces itself, because both return a perfectly plausible number.

Two things follow. An affordability figure has a shelf life measured in weeks, so a number from three months ago is not the number you have now. And the arithmetic runs the other way with equal force: a rate cut lifts the ceiling without anyone earning a cent more, which is why a market can feel suddenly cheaper when nothing about the houses has changed.

A longer term lifts the ceiling too, and it costs far more than it looks. The loan payment calculator shows the total interest sitting behind any monthly payment, which is the figure to check before stretching the term to reach a price.