[print page] Individual Assessment: Exponential Growth To begin your journey, ask yourself, "Why save money?" Is there anything you need to buy in the future that you do not have enough money for today? How will you save this money? How long will it take until you make the purchase? Think about the answers to these questions as you design a scenario. Part I: Scenario You are saving up for a major purchase. The purchase could be college tuition, an entertainment system, a car, or any other purchase you desire. Now it's time to show off your creativity! Create, and submit to your instructor, a fantasy purchase scenario. You must include the responses to each of the following questions about your purchase in complete sentences. What will you buy? (Provide a detailed description of the major purchase.) Why do you want to make this purchase? What is the purchase price? (Choose an amount between $10,000 and $15,000.) Part II: Research Now it's time to find out how much interest you can earn as you save for this big purchase. You will research a compound interest savings account at a local bank or credit union. You may visit the bank and interview a bank teller or pick up a pamphlet. You could also research the bank on the internet. Be sure to follow the guidelines and safety precautions for completing internet searches. Submit the following information about your savings account to your instructor - be sure to include the labels: Name of Bank Name/Type of Account Interest Rate Compounding Frequency Source (e.g., website, teller's name, etc.) Imagine your parent(s)/guardian(s) have offered you a similar savings deal with simple interest. They will pay you the same interest rate as the bank, but they will pay simple interest instead of compound interest. Part III: Calculations and Graphs Compare your options by performing some calculations and creating some graphs. You must show your work on all calculations. For your report, please number your questions - you must show your work on all calculations. 1 Calculate the amount of your compound interest investment after 10 years. Remember that you are starting with $7,500. 2 Calculate the amount of your simple interest investment after 10 years. Remember to use the same rate and compounding as in #1. 3 Create a graph that shows the growth of your compound interest and simple interest investment investment over time. Example of using the tool for compound interest, with a $10,000 principal and a rate of 4.1% compounded daily. Notice that A= was not included, that 10 was used instead of 10,000 (because this graph is scaled in thousands), that a carat symbol ^ (shift-6) was used for exponents, and x was used instead of t. The parentheses are also very important. To copy the graph into your assignment to turn in, go to the File menu in the tool, then select Export > Graphics View to Clipboard. You can then Paste the picture into your document. Created with GeoGebra Part IV: Analysis Now you will compare the two investments. Which is more beneficial and why? Respond to each of the following questions using complete sentences. 1 What is the difference between the graph of a simple interest investment and the graph of a compound interest investment? 2 What is the difference between a simple interest investment and a compound interest investment? 3 About how long will it take for you to save enough money to make your purchase based on the compound interest graph? 4 About how long will it take for you to save enough money to make your purchase based on the simple interest graph? 5 Which investment (simple or compound) is more beneficial and why? 6 In your research, did you find any accounts that offered simple interest? If so, provide a description of where you found them. If not, why do you think were unable to find them? What is one way you could adjust your investment to make your purchase sooner