This activity was developed by a student or students at Mainland High School which is located in Daytona Beach, FL. It is still a "work in progress" with editing and improvements yet to come. 


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, semiannualy, 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 interests 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 semiannualy.
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 twoyear 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.
Principle 
Rate 
Number of interest 
Time 
Amount in account 
Interest earned 
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.
Name of Bank 
Principle 
Number of
Interest 
Time 
Amount in account 
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 2year period?
Carrental 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 permile rate after a certain number of free miles per day. Contact four different carrental companies, and find out their rates for oneweek 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 nonconstant 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.
MathSummer Activity
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