Advanced Algebra College Student Loan Project
Project Write-up Requirements
Due Friday, December 18, 2015
Directions: Title your project and include your name on the front cover. Include the following
parts in your write up.
Part 1 Based on what you’ve read, investigated and what was discussed in class, describe the
college student loan process.
Part 2 The average student debt in Minnesota Colleges in 2014 was $31,579. Assume you
are given a 4 year grace period after college. Your $31,379 in loans are broken down
into 4 types:
 $8000 is a federal loan at 4.76% annual interest compounded monthly.
 $12,000 is a private loan from a local bank at a 11.20% annual interest rate
compounded daily (assume there are 365 days per year)
 $4,000 is a loan at a 14% annual interest rate compounded every hour.
 $7,579 is a loan at a 19% annual interest rate compounded every minute.
How much will you owe for each loan at the end of the 4 year grace period? What is
the total amount of interest accumulated during the 4 year grace period? Show the
mathematics you used in each calculation.
Part 3 For each loan, assume the grace period for repayment is unlimited. How long will it
take for each loan to quadruple in value? Be as specific as possible
(years/months/days) as possible. Show the mathematics you used to find this
amount.
Part 4 Assume the entire $31,579 in debt was one loan at a rate of 9% annual interest
compounded every day. How long will it take until the loan amount reaches
$1,000,000? Show your work.
Part 5 Assume you want to pay off your loans by age 40.
You will begin paying your loans at age 26 after a
4 year grace period. Use the value of the loan
amounts at the end of the 4 year grace period
you calculated in part 2 and the online loan
calculator at
http://www.finaid.org/calculators/loanpayments.phtml
to calculate the amount of your payment for
each loan so that the entire amount is paid off in
14 years. (Note: this calculator assumes the rate of the
loan is compounded continuously like most loans you will get in college. Don’t worry that the loans
above were compounded differently in your prior calculations) Enter the amount of the Loan
Balance, the annual Interest Rate and click ‘calculate’. Record the amount you owe
each month. What is the total amount for all 4 loans per month? Is this amount
reasonable? Why or why not?
Part 6 Reflection– Answer the following questions using full sentences.
 What were the 3 most important things you learned about student loans during
this project?
 What is your advice for any student taking out a college loan?
 What questions do you still have about the college loan project?
 Assume you will attend college someday and you pay for it at least partially
with student loans. What is the maximum amount of student debt you would
feel comfortable with at the end of 4 years of college? Explain why you chose
this amount.
 Assume you will attend college after high school. What information is
important to learn about a college before deciding to attend? What questions
will you ask the admissions office or research online?
 As of today, what are your plans after you graduate high school?
 Is there anything else you want us to know?
Part 7 Attach all homework assignments and class work connected to the student loan
project to the back of your write up.
Continuous compounding[edit]
Continuous compounding can be thought of as making the compounding period infinitesimally small, achieved by
taking the limit as n goes to infinity. See definitions of the exponential function for the mathematical proof of this
limit. The amount after t periods of continuous compounding can be expressed in terms of the initial amount A0 as
It has been shown that the mathematics of continuous compounding is not limited to the valuation of
continuously compounded financial instruments and flow annuities, but rather that the exponential equation is a
versatile model that may be used for valuation of all financial contracts normally encountered.[2] In particular, any
given interest rate (r) and compounding frequency (n) can be expressed in terms of a continuously compounded
rate
:
which will also hold true for any other interest rate and compounding frequency. All formulas involving
specific interest rates and compounding frequencies may be expressed in terms of the continuous interest
rate and the compounding frequencies.