2. Future value The principal of the time value of money is probably the single most important concept in financial management. One of the most frequently encountered applications involves the calculation of a future value. This process requires knowledge of the values of three of The process for converting present values into future values is called compounding four time-value-of-money variables. Which of the following is not one of these variables? The trend between the present and future values of an investment The present value (PV) of the amount deposited The duration of the deposit (N) The interest rate (I) that could be earned by deposited funds 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%, 9%, or 18%. Identify the interest rate that corresponds with each line. VALUE (Dollars) A B 0 1 2 3 4 5 6 7 8 9 10 TIME (Years) Line A: 18% Line B: 9% Line C: 0% Investments and loans base their interest calculations on one of two possible methods: the simple interest and the compound interest methods. Both methods apply three variables-the 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? FV = PV / (1 + I)N FV = PV x (1 + I)N O FV = PV + (PV XIX N) Simple interest? OFV = PV + (PV XIX N) O FV = PV XIXN FV = PV / (PV XIX N) Identify whether the following statements about the simple and compound interest methods are true or false. Statement True False After the end of the second year and all other factors remaining equal, a future value based on compound interest will exceed a future value based on simple interest. O All other factors being equal, both the simple interest and the compound interest methods will not generate the amount of earned interest by the end of the first year. Everything else held constant, an account that earns compound interest will grow more quickly than an otherwise identical account that earns simple interest. Dimitri is willing to invest $45,000 for eight years, and is 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 eight- year investment period, complete the following table and indicate whether Dimitri should invest in each of the investments. Note: When calculating each investment's future value, assume that all interest is earned annually. The final value should be rounded to the nearest whole dollar. Investment Interest Rate and Method Expected Future Value Make this investment? A 10% simple interest $81,000 Yes B 6% compound interest $71,723 No C 7% compound interest $77,318 No