3. Future value "he principal of the time value of money is probably the single most important concept in nancial management. One of the most frequently encountered applications involves the calculation of a future value. "he process for converting present values into future values is called V . This process requires knowledge of the values of three of four timevalueofmone',r variables. which of the following is not one of these variables? 0 The interest rate (I) that could be earned by invested funds 0 The duration of the investment (N) O The ination rate indicating the change in average prices 0 The present value {W} of the amount invested All other things being equal, the numerical difference between a present and a future value corresponds to the amount of interest earned during the deposit or investment period. Each line on the following graph corresponds to an interest rate: 0%, 8%, or 16%. Identify the interest rate that corresponds with each line. 1MLUE [Dollars] i] 'i 2 3 5a 5 '5' H '5' 1|] TIME Wears] LineA: V LineB: V IJ'ne C: v Investments and loans base their interest calculations on one of two possible methods: the V interest and the v interest methods. Both methods apply three variablesthe amount of principal, the interest rate, and the investment or deposit periodto the amount deposited or invested in order to compute the amount of interest. However, the two methods differ in their relationship between the variables. Assume that the variables I, N, and PV represent the interest rate, investment or deposit period, and present value of the amount deposited or invested, respectively. which equation best represents the calculation of a future value (FV) using: Compound interest? 0 FV=PVX{1+I)N O Fv=Pv;[1+1]N OFv={1+1)N;Pv Simple interest? 0 Fv=Pv+(PVxIxN] O FV=PVJ(PVXIXN) OFV=PV[PVXIXN) Identify whether the following statements about the simple and compound interest methods are true or false. Statement True False The process of earning compound interest allows a depositor or investor to earn interest on any interest earned in prior periods. 0 O After the end of the second year and all other factors remaining equal, a future value based on compound interest will O 0 never exceed the future value based on simple interest. All other factors being equal, both the simple interest and the compound interest methods will accrue the same amount of O O earned interest by the end of the first year. Nicholai is willing to invest $30,000 for six years, and i5 an economically rational investor. He has identified three investment alternatives (A, B, and C) that vary in their method of calculating interest and in the annual interest rate offered. Since he can only make one investment during the sixyear investment period, complete the following table and indicate whether Nicholai should invest in each ofthe investments. Note: 1.i'i'hen calculating each investment's future value, assume that all interest is earned annuallv. The nal value should be rounded to the nearest whole dollar. Investment Interest Rate and Method Expected Future Value Make this investment? (n A 8% simple interest V B 3% compound interest C v v C 5% compound interest 3