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 four time-value-of-money variables. Which of the following is not ong compounding The interest rate (1) that could be earned by invested funds discounting The present value (PV) of the amount invested The Inflation rate indicating the change in average prices The duration of the investment (N) 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%, 10%, or 20%. Identify the interest rate that corresponds with each line. VALUE Dollars VALUE IDollar 0 1 2 7 # 9 10 TIHElYears Line A: Line B: Line C: 0% Investmer Joans base their interest calculations on one of two possible methods: the interest and the 10% interest methods. Both methods apply three variables--the amount of principal, the interest rate, and the investment or deposit periodo ount deposited or invested in order to compute the amount of interest. However, the two methods differ in their relationship 20% between bles. Assume that the variables L, 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? O FV = (1 + TN / PV O FV = PV x (1 + 1)N DFV = PV + (PVX1XN) 0 1 2 3 8 9 10 TIME (Years! Line A: Line B: Line C: Investments and loans base their interest calculations on one of two possible methods: the interest and the interest methods. Both methods apply three variables-the amount of the interest rate, and the investment or deposit simple periodto the amount deposited or invested in order to compute the amount of interest. Hq two methods differ in their relationship between the variables. complex 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? O FV = (1 +T)N / PV O FV = PV x (1 +T)N O FV - PV + (PV x 1 x N) C 0 1 2 3 7 8 9 10 TIME IYears Line A: Line B: Line C: interest and the Investments and loans base their interest calculations on one of two possible methods: the Interest methods. Both methods apply three variables-the amount of principal, the interest rate, and the investment or deposit period to the or invested in order to compute the amount of interest. However, the two methods differ in their relationship between the variables. compound uncomplicated pariables 1, N, and PV represent the interest rate, Investment or deposit period, and present value of the amount deposited or cu respectively. Which equation best represents the calculation of a future value (FV) using: Compound interest? O FV = (1 + 1) / PV O FV = PV x (1 + 1) O FV - PV + (PV x 1 x N) invested, respectively. Which equation best represents the calculation of a future value (FV) using: Compound interest? PV = (1 +T) / PV OFV-PVX (1 + 1) OFV-PV + (PV XI X N) Simple interest? O FV = PV + (PV XI X N) O FV-PV(PVX I XN) O FV = PV XIXN Identify whether the following statements about the simple and compound interest methods are true or false. True False Statement All other variables held constant, investments paying simple interest have to pay significantly higher interest rates to earn the same amount of interest as an account earning compound interest. o Everything else held constant, an account that earns compound interest will grow more quickly than an otherwise identical account that earns simple interest. O All other factors being equal, both the simple interest and the compound interest methods will accrue the same amount of earned interest by the end of the first year. Alek is willing to invest $30,000 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 Alek should invest in each of the investments. Note: When calculating each investment's future value, assume that all interest is eamed annually. The final value should be rounded to the nearest whole dollar O FV = PV - (PV XI N) FV - PV XIXN Identify whether the following statements about the simple and compound interest methods are true or false. True False Statement All other variables held constant, investments paying simple interest have to pay significantly higher interest rates to earn the same amount of interest as an account earning compound interest. Everything else held constant, an account that earns compound interest will grow more quickly than an otherwise identical account that earns simple interest. All other factors being equal, both the simple interest and the compound interest methods will accrue the same amount of earned interest by the end of the first year. Alek is willing to invest $30,000 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 Alek 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. Yes No Investment Expected Future Value Make thi: ment? Interest Rate and Method 8% simple interest 3% compound interest 5% compound interest B $