Exponential Function Group Project

 

 

1)  Part #1

            At the reading of the will of your great aunt you find that she left you $10,000 to help you buy a house when you finish your education.  However, your great aunt was very frugal.  The will stipulates to receive the money you must find the bank in your town that gives you the highest interest and you cannot make any withdrawals for 7 years. 

 

            Contact three financial institutions by looking on the internet.  For this assignment, assume that the given interest rates are compounded 1) annually, 2) quarterly, 3) monthly and 4) daily.  Use the table below to record your information (note:  find banks with different interest rates):

 

 

Financial institution

Web address

Interest Rate

1

 

 

 

2

 

 

 

3

 

 

 

 

Based on the given information and the interest data you found answer the following.

 

1.  Choose the bank which will give you the highest interest rate and write the mathematical model. 

 

 

 

 

 

 

 

 

 

 

2.  How much money will you have in the bank in 7 years?

 

 

 

 

 

 

 

 

 

3.  When will your money double?

 

 

 

 

 

Part #2

            You are going to buy a car that will need to be financed.  You will need to look at different options and decide which will be the best choice for your situation.  You will need to find a car on the internet that you want to purchase.

 

Process

 

1.  Find an advertisement for a car that you would like to purchase.  You can look at any internet site, but you might consider:  http://www.edmunds.com to learn how the advertised prices compare with market prices generally for cars of the same make, model and year.

 

2.  Once you have found the automobile you want to purchase and determined how much you will be spending on the car, you need to calculate the monthly payments.  There is an amortization calculator at http://ray.met.fsu.edu/~bret/amortize.html which can help you calculate the monthly payments according the amount you will be borrowing.  Calculate the monthly payment for your car for each option given below.

 

Loan

Interest Rate

Length in Years

1

5%

5

2

7.5%

3

3

9.99%

4.5

4

11.5%

2.5

5

18%

4

 

 

3.  Make a decision as to what you think is the best option and be able to justify your conclusion.  Think about what situations might make you decide not to take each of the following:

 

 

4.  Write up a final report including the following:

 

 

 

 

 

 

 

Part #3

 

Compound Interest and Derivation of “e” Lab

 

The following is to be done in small groups of 4 or 5 using a TI-83 plus calculator. 

 

1.  Suppose that a young couple has $1000 to invest for their child when it is born.  They choose to invest this money in a mutual fund at 12% (annual rate), and they have the option of investing it annually, quarterly, monthly, or daily.  Determine, using both the graphing and table features of your calculator which option will result in the most money after 18 years, what would be the difference in the amounts of money for each option?

 

2.  The group is to write up a summary and present and discuss their findings. 

 

3.  What if we could compound interest for an infinite number of periods?  If we look at

, it can be transformed into by setting .  Graph the expression  for increasingly large values of n.  What does  appear to converge to?  The number that it converges to is called “e”.  So for an infinite number of periods, the formula for compounding interest would be A = Pert and it is called compounding interest continuously.  Redo question 2 and 3 for part 1 using the compounding interest continuously formula.

 

 

 

 

 

 

 

 

 

 

 

 

Adapted from

1)  Exploring Exponential Growth and Decay Functions, by Sharon Nussbaum, Jessica Redlin, and Denise Stewart 

2)  Car Loan Project, by Wendy Clark (http://www.econedlink.org/lessons/inex.cfm?lesson=EM386)

3)  Mount Holyoke’s Laboratory in Mathematical Experimentation, Harriet Pollatsek, Computer Algebra Systems in Education Newsletter, No. 30, January 1998