Keesha is planning a vacation for the summer after she graduates from high school. Her family has agreed to pay for air fare and the hotel accommodations if she saves enough money for the rental car and pocket money. Keesha decides that she will use the money she has saved from her part time job as spending money, and she will use the interest earned in her savings account to pay for the rental car.

Keesha needs to research how much interest she can earn and how much a car might cost to rent. She begins by researching banks and interest rates.

She decides that she wants to deposit $1000 in an account at a bank that pays compound interest. Compound interest is paid on both the principle and any previously earned interest. Banks pay interest on savings accounts at specific interest periods, which can be monthly, quarterly, semi-annually, or annually. Interest rates also vary between banks.

Before she begins shopping for a new bank, Keesha decides to do her own calculations so that she can be more informed when meeting with a banker.

To find the compound interest, she uses the formula    A= P (1+r/n)^nt   where A is the amount in the account, P is the principle, r is the annual interest rate, n is the number of interest periods per year, and t is time in years.

For example, Keesha wants to see how much interest she would earn in two years at a rate of 4% if the interest is compounded semi-annually.

                        A= 1000 (1+ 0.04/2)²⁽²⁾ = 1000 (1+ 0.02)⁴

                                                          = 1000 (1.02)⁴

                                                          = 1000 (1.0824322)  1082.4322

Keesha would earn about $82.43 over a two-year period. She anticipates that the rental car will cost more than $82.43 and decides that her money needs to earn more interest.

Find the amount, A, for each of the following by using the compound interest formula. Assume that there are no deposits or withdrawals after the initial deposit of $1000. Then record your answers in the chart.

1. Find A if P = $1000, r=3%, n=2, and t=2.

2. Find A if P = $1000, r=4%, n=4, and t=2.

3. Find A if P = $1000, r=5%, n=2, and t=2.

4. Find A if P = $1000, r=5.5%, n=12, and t=2.

5. Find A if P = $1000, r=6%, n=1, and t=2.

6. Find A if P = $1000, r=7%, n=2, t=2.

7. Find A if P = $1000, r=8.2%, n=4, and t=2.

8. Find A if P = $1000, r=9%, n=1, t=2.

9.

Call or visit at least five banking institutions in your community. Find out their policies on compound interest. Then calculate the interest earned on $1000 over 2 years at their given rates and number of interest periods per year. Complete the chart.

10.

11. Using the information in the chart, what is the average interest rate that most banks offer?

12. About how much interest do you think Keesha will earn over a 2-year period?

Car-rental companies usually charge a flat rate per day or a special weekend rate. In addition, some companies offer unlimited miles, and some charge an additional per-mile rate after a certain number of free miles per day. Contact four different car-rental companies, and find out their rates for one-week rental of a compact car. Try to get a variety of rates and billing conditions. Record your information in a table of values. Then graph the ordered pairs on the grids provided.

13. Name of car rental company: _____________________________

14. Name of car rental company: _____________________________

15. Name of car rental company: _____________________________

16. Name of car rental company: _____________________________

17. Which graphs represent linear functions? Why?

18. Which graphs represent non-constant linear functions? Why?

19. Review all of the data you have gathered. What recommendation would you make to Keesha about making a rental car choice based on the price of the rental car and the amount of money she can afford to pay for it? Explain your response.