A Financial Model on Costs to Students
from
Eliminating Student Loan Subsidies
Introduction: Currently, lowincome undergraduate students
can take out a total of $31,000 in federal student loan. Subsidized student loans are only available
to people in lowincome households. The main
difference between subsidized and unsubsidized student debt is that the
government pays all interest costs on subsidized debt when the student is in
school while interest accrues on unsubsidized loans.
The current limit on subsidized student loans
is $23,000. The total limit on
undergraduate federal student loans is $31,000.
The Trump Administration is
proposing to eliminate all subsidized student loans.
The purpose of this post is
to model and analyze the impact of this
policy change for a student who is planning to take full advantage of subsidized
student loans. I also examine how this
financial cost depends on the number of years it takes for the student to
graduate.
Methodology: I set up a spread sheet where the key model
inputs are number of years it takes for a student to graduate, the interest
rate on the student loan, and the maturity of the student loan.
Key Assumptions:
In this model, I assume the student borrows
$31,000/n each year where n is the number of years it takes for the student to
graduate. When subsidized loans exist
the annual total borrowed for subsidized loans is $23,000/n and total
unsubsidized loans for the course of the person’s undergraduate career is
$8,000.
(An expanded version of this model will consider
uneven borrowing scenarios, where student borrows a different amount each year
or perhaps drops out from school for a few years.)
Student remain in deferment
until six month after graduation or leaving school.
Student does not apply for loan
deferments for economic hardships or when unemployed.
The interest rate is 5
percent.
Student loan maturity is 20
years.
The procedure to calculate lifetime costs involves two
steps.
Step One: Calculate
the total loan balance on the day the student borrower starts repayment. The subsidized loan at time of repayment is
equal to the balance when issued since all interest is paid for. The FV of the
unsubsidized loan is determined at time of graduation and multiplied by
(1+0.05)^{0.5} to account for the sixmonth delay in repayment after
graduation.
Inputs of FV function:
INT interest rate 0.05 or
some other assumption.
NPER number of periods in
this case number of years in school.
PMT is payment in this case
the annual loan amount.
PV in this case 0
Type is ! for end of period.
The FV gives the value of the
loan at graduation. Repayment is six
months later. The value of the loan at
repayment is FV^{0.5}
The total loan balance is the
sum of the subsidized and unsubsidized loan balance at time of repayment.
Step Two: Calculate total payments over the lifetime of
the loan. This is done by using PMT
function to get monthly payment and then multiplying by the total number of
payments.
Spreadsheet for person who graduates in four years:
row

Subsidized Loans

No Subsidized Loans


2

Date of First Loan Payment

9/1/10

9/1/10

3

Subsidized Loan

$23,000

$0

4

Unsubsidized Loans

$8,000

$31,000

5

Interest Rate

0.05

0.05

6

Number of years In school

4

4

7

Date Repayment Starts

3/2/15

3/2/15

8

FV of subsidized loans

$23,000

$0

9

FV of unsubsidized Loans

$9,275

$35,940

10

Total Loans

$32,275

$35,940

11

Loan Maturity

20

20

12

Loan PMT

$213

$237

13

Lifetime Payments

$51,120

$56,925

· The elimination of subsidized loans increases lifetime
repayment costs of the loan by $5,805 when the person graduates in four years
and starts repayment six months after graduation. (The other key assumptions are a 5% student
loan interest rate and a 20year student loan.)
Impact of delays in finishing schools:
The addition cost stemming
from the loss of the subsidy can be obtained by changing line 6 of the
spreadsheet number of years in school.
Below we present results for # of years in school for 4, 5, and 6.
Calculations are below:
# of Years in School

Payments with Subsidized Loans

Payments with No Subsidies

Difference

4

$51,119.83

$56,924.81

$5,805

5

$51,496.04

$58,382.62

$6,887

5

$51,884.94

$59,889.61

$8,005

· The elimination of subsidized loans leads to even higher
costs for the person who spends more years in school. Additional lifetime costs of loans are
$6,887 for the person who graduates after 5 years and $8,005 for the person who
graduates after six years.
Authors Note: I will soon create additional Excel Finance
problems involving the elimination of subsidized student loans. The problems will involve students who
borrow different amounts each year, take some time off from school, or obtain
additional loan deferments to obtain graduate school.
This problem is question 17
on the Excel finance tutorial.