A common question from borrowers is how much house can they qualify for. The answer to this question takes some work since there are a number of variables that must be accounted for. Interest rates, down payment size and lender DTI restrictions all play an important part.
To start with, let's assume an income of $60,000, or $5,000 per month. To simply things we will assume that there is no other monthly debt. I will show how to take other debt into account as we go along.
The maximum allowable DTI (debt to income) ratio varies from lender to lender, with some sub prime lenders allowing as high as 50-55%. For conforming loans the standard is 36%, so we will use that in our example. A DTI of 36% means that your mortgage payment can be as high as 36% of your $5,000 income, or $1,800. If you have other monthly debt you will need to subtract that from this number. What is left is your maximum monthly mortgage payment.
To turn a monthly payment into a loan amount we need two things: interest rate and loan term. To maximize buying power you want the term as long as possible. Normally this is 30 years, though many lenders now offer some sort of 40 year product. Since a 30 year term is the most common and is available from any lender we will use that in our calculations. For an interest rate we can check the going rate for a 30 year fixed product, which at the time of this writing is about 6%. This rate will definitely change based on creditworthiness, so adjust it up or down based on your credit.
The formula for loan amount from a monthly payment is the inverse of the formula for monthly payment from loan amount that we looked at last time:
Payment = Loan Amount * ((I)(1+I)^N) / (((1+I)^N) - 1)
Loan Amount = Payment * (((1+I)^N) - 1) / ((I)(1+I)^N)
Recall that I is the interest rate per payment period as a decimal and N is the number of payments.
For the numbers we chose above we get:
Loan Amount = 1,800 * ((1.005^360) - 1) / ((.005)(1.005)^360) Loan Amount = 1,800 * 5.02257 / (.005)(6.02257) Loan Amount = $300,224.85
The final step is to factor in the size of the down payment. You can do this in two ways, depending on how much money you have on hand. If you have a set amount, such as $30,000, that you have set aside for your down payment, then simply add this to the loan amount and you have your maximum house price. If you have enough money to specify a percent down payment, such as 10%, then divide your loan amount by the LTV (100 - down payment %). For the numbers in our example this is $300,244.85 / .9 = $333,583.17.
As you can see we are forced to make some assumptions, such as the interest rate and allowable DTI, but once we do this we are able to get a reasonable estimate as to how much house you can afford (or at least qualify for). |