Wednesday, January 11, 2017

Trend Growth of Undergraduate Student Debt

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 Four-Year 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 Four-Year 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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