Question Six: A person with a $100,000 student loan with a
10year term at a 6% interest rate and no other debts is applying for a
mortgage. In order to qualify for the
mortgage two constraints must be satisfied.
First, total mortgage interest must be less than 28% of monthly
income. Second, total interest payments
from all sources must be less than 38% of monthly income.
What monthly income does this person need in order to qualify
for a $300,000 mortgage if the mortgage interest rate on a 30year FRM is
4.25%?
How much income does the person need to qualify for the same
loan if the student loan is converted to a 20year term?
Answer: First, calculate the monthly mortgage
payment, the monthly student loan payment and the total monthly debt payments
on both loans.
Second, calculate income consistent with the requirement
that the monthly mortgage debt be no more than 28% of monthly income. This income is MORT DEBT/0.28.
Third, calculate the income consistent with the requirement
that all monthly debt payments be no more than 38% of monthly income. This income is TOTAL MONTHLY DEBT
PAYMENTS/0.38.
The required income is the maximum of the income required
from the two constraints.
The restructuring of the student loan changes the monthly
income needed to qualify for the mortgage from $6,806 to $5769. See table below for the calculation.
Student Debt and Mortgage
Qualification


Student Debt at 10 Years

Student Debt at 20 Years

Comment


Student Loan Amount

$100,000

$100,000

Assumption

Interest Rate

0.06

0.06

Assumption

Number of Student Loan
Payments

120

240

Assumption

Student Loan Payment

$1,110

$716

From Payment Function

Mortgage Amount

$300,000

$300,000

Assumption

Mortgage Interest Rate

0.0425

0.0425

Assumption

Term

360

360

Term

Mortgage Payment

$1,476

$1,476

From Payment Function

Total Monthly Debt
Payment

($2,586)

($2,192)

Sum of Monthly Mortgage
and Student Debt Payments

Constraint One: Absolute
Value of Mortgage Payment Divided by 0.28

$5,271

$5,271

Calculation

Constraint Two: Absolute
Value of Monthly Debt Divided by 0.38

$6,805

$5,769

Calculation

Required Monthly Income

$6,805

$5,769

Max of two constraints

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