Question Eight: A person has a $80,000 student loan at a 7.0% interest
rate. The student debt is the person’s
only debt. The person can set the term
of the loan at 10 years or 20 years.
The person makes $95,000 per year.
The person is seeking a mortgage.
The mortgage payment must be less than 28% of monthly income. In addition, total monthly debt payments
must be less than or equal to 38% of monthly income. The current mortgage rate is 4.5%.
Create a spreadsheet
that calculates the amount of mortgage this person can qualify for if the
student loan is set at a 10year term and if the student loan is set at a
20year term.
How much mortgage can the person qualify for at current
interest rates?
How much mortgage could the person qualify for if the
student loan interest rate rose by 10%?
How much mortgage could the person qualify for if the
mortgage rate rose by 10%?
Answer: First, I find the maximum allowable monthly
mortgage payment. Second, I find the
mortgage balance consistent with this monthly payment given current interest
rates and the term of the loan.
The maximum allowable monthly mortgage payment is the
minimum of 28% of monthly income or 38% of monthly income minus monthly
consumer debt payments.
In this problem the only consumer loan is the student loan.
Note that when the student loan term is 10 years the binding
constraint is monthly payments less than 38% of monthly income. However, when the student loan term is 20
years the binding constraint is mortgage payment less than 28% of monthly
income.
The allowable mortgage is the present value of the allowable
maximum monthly payment. The PV
function depends on the interest rate, the term of the loan, and the payment.
Note that
PV(0.045/12,360,$2079)= $410,406
Note also that PV(0.045/12,360,$2217) = $437.484.
The conversion of the student loan from a term of 10 years
to a term of 20 years allows this person to qualify for around $27,000 more in
mortgage.
The spreadsheet is set up so it is easy to examine how
different mortgage or student loan details impact the allowable mortgage. The problem asks us how to consider how a
10% change in student loan rates or a 10% change in mortgage rates would impact
the allowable mortgage.
Impact of a 10%
increase in student loan rates:
·
The allowable mortgage for the person with a
10year student loan fell by around $6,000 after the student loan interest rate
was increased by 10%.
·
The allowable mortgage for the person with a
20year student was unchanged in response to a 10% increase in the student loan
rate. This occurred because even at the
higher student loan interest rate the requirement that mortgage debt be no more
than 28% of income remained the binding constraint.
Impact of a 10% increase in Mortgage Rates:
·
A 10% increase in mortgages results in a 5.1%
decrease in the allowable mortgage for both the person with a 10year student
loan and a 20year student loan. This
result makes sense since the mortgage debt constraint is the binding constraint
on how much this person can borrow.
Calculation of Maximum
Allowable Mortgage


Student Loan interest
Rate

0.07

0.07

Assumption

Student Loan Term

120

240

Assumption

Student Loan Amount

$80,000

$80,000

Assumption

Payment on Student Loan

$929

$620.24

Calculation from PMT
function

Annual Income

$95,000

$95,000

Assumption

Monthly Income

$7,917

$7,917

Calculation

28% of Monthly Income

$2,217

$2,217

Calculation: This is the
first constraint

38% of Monthly Income 
Consumer Debt Payments

$2,079

$2,388

Calculation: This is the
second constraint

Maximum allowable monthly
mortgage payment

$2,079

$2,217

Calculation: The maximum allowable monthly mortgage
payment is the smaller of the amount allowable from the two constraints.

Mortgage Interest Rate

0.045

0.045

Assumption

Mortgage Term

360

360

Assumption

Allowable Mortgage

$410,406

$437,484

Calculation: From PV function

Other financial math problems can be found here.
I am also doing work comparing costs of schools and salaries of future graduates of schools. The post below looks at some data for Big Ten schools.
http://policymemos.blogspot.com/2016/05/informationonbigtenschoolsfrom.html
It might be useful to combine information about median salaries and median debts from different schools to figure the maximum amount of house that a typical graduate from each school could purchase. The data on student debt is somewhat limited because it does not include private loans or PLUS loans taken out by parents. Despite these limitations more on the nexus between housing markets and the cost of college will follow.
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