Trend Growth of Undergraduate Student Debt
Question: The table below has average debt of
undergraduates who borrowed while getting a Bachelor’s degree and the percent
of bachelor degree recipients who borrowed.
Based on this data what is the expected total debt borrowed
by 100,000 recipients of Bachelor’s degrees in the two years?
What is the average annual change in average debt, % of
Students who borrowed, and total debt?
Assume that all variables continue to grow at the same
average annual rate. Under this
assumption, what is the average debt, percent of students borrowing, and total
debt in 2016 if these growth trends continued?
Amount Borrowed by Undergraduates Receiving a Bachelor's Degree
from a FourYear University


2003/2004

2011/2012


Average Debt for Borrowers

12,876

20,163

% of Students who Borrowed

60.8

65.2

Source of data is NSPAS files obtained at https://nces.ed.gov/datalab/
Analysis: The expected number of students who borrowed
based on a total of 100,000 students is the percent that borrowed multiplied by
100,000. Take this number and multiply
by average debt to get expected debt from a random population of 100,000
students.
Amount Borrowed by Undergraduates Receiving a Bachelor's Degree
from a FourYear University


2003/2004

2011/2012


Number of Students

100000

100000

Average Debt for Borrowers

12,876

20,163

% of Students who Borrowed

0.60810

0.65186

Total

7.8E+08

1.3E+09

In order to get the average annual percentage change for the
variables use the formula: g=(F/S)(^{1/8})1
In this formula, F is the final value in 2011/2012 and S is
the starting value in 2003/2004.
Once you get g use the formula F=S*(1+g^{)8} to get
the projected value for 2019/2020.
Here S is the value of the variable that exists in 2011/2012
and F is the terminal value for 2019/2020.
(g the average annual growth rate.)
Here are the projections of the three student debt values in
2020 under the assumption that the average annual percentage change in the
variables remains at the level that existed between 2003/2004 and 2011/2012.
Student debt projections for 2020 assuming constant
average
annual percent change in debt variables


2003/2004

2011/2012

Average Annual Percentage Growth

Projection for 2020


Number of Students

100000

100000

NA


Average Debt for Borrowers

12,876

20,163

5.8%

31,574

% of Students who Borrowed

0.60810

0.65186

0.9%

0.698764763

Total

7.8E+08

1.3E+09

6.7%

2.2E+09

This is not a pretty picture. Obviously debt levels won’t grow at this
rate forever but eight years is not forever.
Even if the growth in the debt rates were reduced by half this growth
rate would be well above recent changes in wages.
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