B-29. SAVING FOR COLLEGE ? ? ? 21 Suppose you have $1000 to invest and know of two investment options. You can invest in bonds (which pay 8% simple interest) or put your money in a credit union account (which pays 8% compound interest). Will the option you choose make a difference in the amount of money you earn? Examine these two situations below. Bonds with Simple Interest: VALUE OF BONDS a. If you invest in bonds, your $1000 would grow as shown in the table at right. How does money grow with simple Amount of Money interest? Number of Years (in dollars) b. By what percent would your balance have increased at the 4" year? Show how you know. 1000.00(initial 0 value) 1080.00 2 1160.00 3 1240.00 4 Accounts with Compound Interest: VALUE OF CREDIT-UNION ACCOUNT c. Instead, if you invest your $1000 in the credit union at 8% compound interest that is compounded once a year, its Amount of Money Number of Years value would grow as shown in the table at right. Why is there $1166.40 in your account at the second year? Explain (in dollars) how the compound interest is calculated. How is it growing? 0 1000.00 (initial value)Accounts with Compound Interest: VALUE OF CREDIT-UNION ACCOUNT c. Instead, if you invest your $1000 in the credit union at 8% compound interest that is compounded once a year, its Amount of Money Number of Years value would grow as shown in the table at right. Why is there $1166.40 in your account at the second year? Explain (in dollars) how the compound interest is calculated. How is it growing? 0 1000.00 (initial value) d. What will be the balance of the credit-union account at the 4" year? By what percent would this account balance 1080.00 increase at four years? Show how you know. 2 1166.40 e. Which type of account - a bond with simple interest or a credit union account with compound interest - grows most 1259.71 quickly? 4B-30. Assume that the interest is added at the beginning of a new year. Make one graph that shows how each type of investment (simple and compound) starts with $1000 and grows over 8 years. Discuss these questions in your team as you graph: Discussion Points Can I make the graph clearer with color? What happens to the money in between the years? How can I represent the "between" amount on a graph? B-31. In the previous chapter you used models as an estimate of real behavior. Creating a best-fit line for scattered data is one example of a model. Models give you a mathematical way to describe the data and to make predictions. BANK The simple and compound interest situations in problem B-30 were both step functions. Writing equations for step functions can be very complicated. However, you can model the step functions with other equations with which you are already familiar. a. Think about the growth and the starting point for the simple and compound interest situations from this lesson. Model each of the two step functions with an equation. Let y represent the money in the account after a years. b. Check that your equation represents the tables in problem B-29. If your models do not match the tables, correct your equation. c. Use your model to predict how much your original $1000 investment would be worth at the end of 20 years in the credit union. d. Why are the equations considered models, instead of representations of the real behavior? Is there an advantage to using the model to make predictions?B-32. In this course, use continuous functions to model situations, unless indicated otherwise. A third option for investing money is a money market account, which offers 8% annual interest compounded quarterly (four times per year). This means that the 8% is divided into four parts over the year, so the bank pays 2% every three months. FOR MY a. Model the value (every three months) of the $1000 investment in this money market account with an equation. Let y represent the money in the account MONEY MARKET ACCOUNT after x quarters. b. Use the model to find the value of your $1000 investment at four years. How does this compare with your other investment options from problem B-29?Read Problem Value of Bonds Years $ 0 1.000.00 (Initial amount) 1 1.080.00 2 1,160.00 3 1,240.00 4 B-29 from the eBook: Simple Interest a.) Describe how the money grows? = b.) By what percent will your balance have increased by year 47 EXPLAIN how you know. k] - M | Read Problem B-29 from the eBook: Compound Interest Value of Credit Union Account d.) [Part 1] What will be the balance of this account in year 47 Years $ 1.000.00 (Initial amount) 1 1,030.00 2 1,166.40 [a] Y Vi 3 1259.71 4 d.) [Part 2] What is the percentage of increase? Demonstrate how you know. c.) Describe how the money grows? Read Problem B-29 from the eBook: Simple Interest vs. Compound Interest Reflection 1)Which account grows quicker? A bond with Simple Interest or a credit union account with compound interest? @] Read Problem B-30 from the e Book: Graphs of Simple and Compund Interests / Tr Vi & ev o Make a graph that shows each investment's starting amount F1500 F1000 and growth over 8 years. Keep the following points in mind as you create your graph: 1) How can you use color to make the graph clearer? 2) What happens to the money in between the years? 3) How can you represent the "between" amount on a graph? Read Problem B-31(a) from the eBook: Modeling with Equations Simple Interest Equation: Compound Interest Equation: Submit SubmitRead Problems B-31 (c) and (d) from the eBook: Modeling with Equations c.) Use your model to predict how much your investment is worth at the end of 20 years in the credit union. d.) [Part 1] Why are the equations considered models, instead of representations of the real behavior? @ v w d) [Part 2] Is there an advantage to using the model to make predictions? Read Problem B-32 from the ebook: Annual Interest Compounded Quarterly a.) Write an equation to model the investment value. b) [Part 1] Use the equation to find the value of your investment at 4 years. [a] Y Vi b) [Part 2] How does this value compare with the other investments options from problem B-297