Exercise: Federal student loan

Learning about annuities can be dry when students cannot relate to the concept. However, since many students have student loans, this is an ideal context to study annuities and interest rates. I therefore present my students with the following exercise, to be solved in class while working in pairs.

Year in college Amount borrowed Interest rate
1 $3,500 3.4%
2 $4,000 3.4%
3 $5,000 3.86%
4 $5,000 4.66%

Additional information

  • The interest rate is fixed for the life of the loan
  • The DoE pays the interest on subsidized loans while you’re in school
  • The student chooses the standard repayment plan
    • Payments are a fixed amount of at least $50 per month
    • Up to 10 years
  • Interest rates are APRs with monthly compounding
  • A consolidation loan has a fixed interest rate which is the weighted average of the interest rates on the loans to be consolidated
  • All education loans allow for penalty-free prepayment

Questions

  • How much do you owe after graduating?
  • What is the consolidated interest rate?
  • How much do you have to pay each month if you want to pay off the consolidated loan in five years?
  • Assume you can pay $200 per month. How long does it take to pay off the consolidated loan? Hint: use NPER()
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