Attention: Due to a bug in Google Chrome, this page may not function correctly. Click here to learn more. Aa Aa 2. Introduction to the future value of money Under the concepts of the time value of money, you can determine the future value of an amount invested today that will earn a given interest rate over a given amount of time. This technique can be used to calculate the future value of (1) a single receipt or payment made or (2) a series of receipts or payments Devin and Noah are sitting together, with their notebooks and textbooks open, at a coffee shop. They've been reviewing the latest lecture from Dr. Boudreaux's financial management class by asking each other questions. Today's topic addressed the calculation of future values for both simple and compound interest-earning accounts. Complete the missing information in the conversation that follows. Round your final answer to all computations to two decimal places. However, if you compute any interest factors as an intermediate step in your calculations, round them to four decimal places. Devin So, why is it important to be able to calculate the future value of some amount invested? , and the Noah First, remember that the amount invested is usually called amount earned during the investment period is called calculate a future value so that you can know in advance what a given amount of principal will be . It is important to be able to for a known worth after earning a specified Devin OK, I understand that, and I know the amount of principal invested today can be called the value of the investment, whereas the amount realized after the passage of t period of value. But what causes the present and future values to be different time is called its values? Noah Two things cause the present and future values to be different amounts. First, the earned during the investment period causes the future value to be greater than, equal to, or less than the present value. Second, the method used to calculate the interest interest-determines the earned-that is, whether the account pays amount by which the future value differs from the present value. Devin That makes sense, and I remember Dr. Boudreaux saying that the difference between simple and interest, interest is earned solely on the compound interest is that in the case of interest, interest is earned not only on the invested principal, but in the case of principal but also on previously earned interest. Noah Very good! So, here's your next question. Assuming equal amounts of principal, interest rates, and investment periods. which tvpe of account should oroduce the areater future value: the Ch 05: Assignment - Time Value of Money equai to, or less than the present value. Secona, tne metnoa usea to caicuiate the interest interest-determines the earned-that is, whether the account pays amount by which the future value differs from the present value. Devin That makes sense, and I remember Dr. Boudreaux saying that the difference between simple and interest, interest is earned solely on the compound interest is that in the case of interest, interest is earned not only on the invested principal, but in the case of principal but also on previously earned interest. Noah Very good! So, here's your next question. Assuming equal amounts of principal, interest rates, and investment periods, which type of account should produce the greater future value: the account earning simple interest or the account earning compound interest? interest should have the greater future Devin By my reasoning, the account earning value, assuming identical amounts of principal, interest rates, and investment periods. Noah Again, correct! But now, I want you to prove it. So let's assume that you invest $2,000 into two different accounts, both of which earn 11% per year, and the money is invested for three years. Account A earns simple interest, while account X earns compound interest. By how much will the future value of account X exceed the future value of account A? Here is a sheet of paper. Show me how to calculate the future values of the two acco ccounts. Devin OK, let me see what I can do. .. Future Value of Account A Note: Account A pays simple interest. Principal +Interest Future ValueA Principal [(Principal x Interest Rate) x Investment Period] $2,000 [($2,000 x 11% ) x 3 years] - $ Future Value of Account X Note: Account X navs.comnound interest. Test-Bank-Ch-5 docx. Ch 05: Assignment- Time Value of Money [(Principal x Interest Rate) x Investment Period] Principal + $2,000 + [($2,000 x 11% ) x 3 years] Future Value of Account X Note: Account X pays compound interest. Future Valuex Present Value x Interest Rate Factor Present Value x (1 + Interest Rate) N $2,000 x (1 +0.11)3 To find the interest rate factor, you can use four different methods, including multiplying it out: (1+0.11) x (1 + 0.11) x (1 + 0.11)1.3676 Interest Factor Or you can use exponents and calculate it directly: Interest Factor = (1+0.11)3 1.3676 The third alternative for solving the equations is to use a spreadsheet, and the fourth is to let a financial calculator perform the calculation. This requires that you know how your calculator functions and how to enter the following variables: Input 1 3 11% 2000 Keystroke P/Y N T PV FV Output Answer P/Y indicates the number of compounding periods per year, N is the number of years, I is the interest rate, PV is present value, and FV is future value. Difference in Future Values FVx FVA Difference Devin So, what do you think? Noah Your work looks fantastic! Test-Bank-Ch-5.docx and how to enter the following variables: 3 Input 1 11% 2000 Keystroke P/Y I FV N PV Output Answer P/Y indicates the number of compounding periods per year, N is the number of years, I is the interest rate, PV is present value, and FV is future value. Difference in Future Values Difference FVx FVA Devin So, what do you think? Noah Your work looks fantastic But now I've got to challenge you with one last question: What would happen to the value numbers and the difference between them if the two accounts did not pay interest? two future Devin Uh. . . if the interest rate were zero, then interest would earned by ; the future value of account A would be ;the future value of account X would be and the difference between the two accounts would be Noah Correct! You are so ready for Dr. Boudreaux's next quiz. en