Previous posts asked how much income would be needed for a
person to qualify for a particular mortgage.
http://www.dailymathproblem.com/2019/06/studentdebtandqualifyingfor.html
http://www.dailymathproblem.com/2019/06/studentdebtandqualifyingfor.html
This post asks how much house a person with a particular
income buy. I assume he has a large
student loan, which can be set to a 10year or 20year term.
Situation:
Consider a person with a $100,000 student debt. The person can either pay the debt back over
a 10year period or a 20year period.
The student loan is this person’s only consumer debt.
The person earns $80,000 per year.
The student loan interest rate is 7.0 percent.
The mortgage interest rate is 4.0 percent.
The mortgage term is
30 years.
Questions:
How much mortgage can the person qualify for if the person
keeps the student loan at 10 years?
How much mortgage can the person qualify for if the person
changes the student loan term to 20 years?
What is the increased cost of the student loan payments
involved by switching from a 10year to 20year student loan?
Answer: I developed a spreadsheet that calculates
the maximum allowable mortgage this person can qualify for.
In order to qualify for a mortgage two conditions must hold.
Monthly mortgage payments must be less than 28% of income.
Monthly mortgage and consumer loan payments must be less
than 38% of income.
First, I calculate the maximum allowable mortgage payment
based on zero consumer debt. This value
is 28 percent of monthly income.
Second, I calculate the maximum allowable mortgage payment
consistent with mortgage payments and consumer debt payments equal to 38
percent of income. This is done by
backing out the consumer loans and allocating the rest to mortgage debt.
I insert mortgage interest rate, term and payment info into
the PV functions to get the mortgage amount
The allowable mortgage is the minimum of the mortgage totals
consistent with the two constraints.
The calculations for the two situations presented in this
problem are presented in the table below
Mortgage Qualification
Example for Borrower with Student Debt


row #

Student Loan Information

Note


1

Student loan Amount

$100,000

$100,000

Assumption

2

Interest Rate

0.07

0.07

Assumption

3

Number of Payments

120

240

Assumption

4

Student Loan Payment

$1,161

$775

From PMT Function

Mortgage Information


5

Rate

0.035

0.035


6

Term

360

360


Income Assumption


7

Income

$80,000

$80,000

Assumption

8

Constraint One: Maximum monthly mortgage payment consistent
with this income assumption

$1,867

$1,867

28% of monthly income

9

Constraint Two: Maximum monthly consumer and mortgage
payments consistent with income

$2,533

$2,533

38% of monthly income

10

Maximum mortgage
consistent with constraint one.

$415,697

$415,697

pv of mortgage rate
number of periods, and pmt where mortgage rate and payments are assumptions
baed on the market and product chosen and payment is max allowable given
income

11

Allowable mortgage
payment consistent with constraint two given required student debt

$1,372

$1,758

Row 9 minus Row 7

12

Max mortgage consistent
with borrowing contraint two.

$305,593

$391,505

Use PV function with rate
and term set by market and product and payment the amount of mortgage payment
after required consumer payments

13

Allowable mortgage debt

$305,593

$391,505

Minimum of Row 10 and Row
12

An increase in the term of the student loan from 10 to 20 years
increases the size of a mortgage a household can qualify for from $305,000 to
$391,000.
Getting the extra mortgage is not cheap. The increased student loan term causes total
student loan payments to go from $139.000 to $186,000.
Concluding thoughts: Most people who have $100,000 in student debt
will have to refinance the student loan if they are going to buy a house.
Another strategy that needs to be considered is delay for
five years pay off as much of the student loan as you can and then buy.
The problem is even more complex for people with other
consumer loans like credit cards and a smaller amount of student debt. In this case, refinancing the student loan
does not increase the amount of mortgage a person can qualify for by that much.
A discussion of mortgage qualification when a borrower has
less student debt but additional consumer loans can be found at the post below.
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