Tuesday, November 17, 2015

Question Six: Income Needed to Qualify for a Mortgage for a Person with Student Loans

Question Six:  A person with a $100,000 student loan with a 10-year 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 30-year 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 20-year 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

Other financial math problems can be found here.
http://financememos.blogspot.com/p/financial-math-in-excel.html

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