# One Person’s Misery Is Another Person’s…Math Problem

Hat tip to Rob Carrick of Globe and Mail for pointing out a CNN story titled “I’m 57 and owe \$152,000 in student loans,” which he described as “student loan hell.”

I thought this story which traces the travails of a Rosemary Anderson would be a way to engage students both to the dangers of student loans but also how compound interest can work against you if you are a borrower not making payments on a loan.  It also will provide students the chance to hone their analytical skills (and wonder why some of these numbers don’t seem to add up!).

So, how might I think about structuring this activity?

1. Read the article
2. Jot down key facts about the case that will help you run some calculations.  A timeline should help:
1. Age 37 and 44 gets bachelor and master’s degree in human resources; incurs \$65,000 in debt.
2. At age 44, consolidated all loans (\$65,000) into one loan with interest rate of 8.25%
3. At age 51 (six years ago), she stopped making payments on her loans.
4. At age 57 (today), owes \$152,000 in student loans
5. April, 2016 (when she is 58) Scheduled to make payments of \$699 per month until age 81 (for 23 years)

Questions for students:

1.  At age 44, she had \$65,000 in loans; 13 years later (at age 57) she had balances of \$152,000.  What happened?  Use this compound interest calculator and assume starting loans of \$65,000; interest rate of 8.25% and term of 6 years (she said she made payments until six years ago and I am being conservative in assuming that she made little headway on reducing her loan balances before then). What would her balance have been if she made no payments for those six years?

2.  Why do you think this amount is lower than the \$152,000 headline?  A few possible explanations:

• She made payments from age of 44 to 51 but they weren’t large enough to reduce her principal balance which continued to grow
• Penalties for non-payment of her student loans added to hear loan balances over time

3.  What would the monthly payment on her loan be: assume a balance of \$152,000, interest rate of 8.25% and 23 year term?

Our trusty loan calculator, spits out an answer of \$1,231…hmmm, but the article says that she would only need to be paying \$699/month for the next 23 years (starting next April) and laments the fact that she is not able to refinance at a rate lower than 8.50%.  Something doesn’t seem to be adding up….anyone have an explanation?

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When you don’t have an answer to a student loan question, you just ask Mark.  Mark Kantrowitz of Edvisors, that is.  Here is his answer as to the potential reasons why the numbers don’t add up (thanks Mark!):

Likely causes include:
1. The borrower may be reporting \$65,000 as the amount borrowed (disbursed), not recognizing that interest accrued during the in-school period and is capitalized at repayment. So she may have owed more than \$65,000 at age 44.
2.  The loans are all federal, based on the 8.25% interest rate and the statement in the article that loans were consolidated with the U.S. Department of Education. In other cases, borrowers of defaulted private non-federal loans may have collection charges added to the loan balance. This only happens with federal loans when defaulted loans are rehabilitated (e.g., 18.5% added to the loan balance).
3. Aside from this, though, to increase from \$65,000 to \$152,000 at 8.25% will require 10.7 years, compounded annually, 16 years without compounding, despite only 13 years available.
4.  Age 58 to 81 is 23 years. Most likely this is 25 years. Extended repayment of \$152,000 would involve \$1,198 per month, not \$699. Even if there’s a digit transposition, \$125,000, that is still \$986 per month. So that leaves IBR and ICR as the main possibilities. For IBR to yield \$699 would require annual income AGI of \$73,572, which is a little high for a monthly take home pay of \$3,400, but not too high. ICR requires \$53,710. Both could work.