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Chapter 09: Time Value of Money Chapter 9 Time Value of Money Discussion Questions 9-1. How is the future value (Appendix A) related to the present value of a single sum (Appendix B)? The future value represents the expected worth of a single amount, whereas the present value represents the current worth. FV = PV (1 + I ) n future value ( 29 lue Present va 1 1 FV PV + = n i 9-2. How is the present value of a single sum (Appendix B) related to the present value of an annuity (Appendix D)? The present value of a single amount is the discounted value for one future payment, whereas the present value of an annuity represents the discounted value of a series of consecutive future payments of equal amount. 9-3. Why does money have a time value? Money has a time value because funds received today can be invested to reach a greater value in the future. A person would rather receive $1 today than $1 in ten years, because a dollar received today, invested at 6 percent, is worth $1.791 after ten years. 9-4. Does inflation have anything to do with making a dollar today worth more than a dollar tomorrow? Inflation makes a dollar today worth more than a dollar in the future. Because inflation tends to erode the purchasing power of money, funds received today will be worth more than the same amount received in the future. 9-1
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Chapter 09: Time Value of Money 9-5. Adjust the annual formula for a future value of a single amount at 12 percent for 10 years to a semiannual compounding formula. What are the interest factors (FV IF ) before and after? Why are they different? ( 29 Semiannual 3.207 20 n 6%, i Annual 106 . 3 10 n %, 12 i A Appendix FV PV FV IF = = = = × = The more frequent compounding under the semiannual compounding assumption increases the future value so that semiannual compounding is worth .101 more per dollar. 9-6. If, as an investor, you had a choice of daily, monthly, or quarterly compounding, which would you choose? Why? The greater the number of compounding periods, the larger the future value. The investor should choose daily compounding over monthly or quarterly. 9-7. What is a deferred annuity? A deferred annuity is an annuity in which the equal payments will begin at some future point in time. 9-8. List five different financial applications of the time value of money. Different financial applications of the time value of money: Equipment purchase or new product decision, Present value of a contract providing future payments, Future value of an investment, Regular payment necessary to provide a future sum, Regular payment necessary to amortize a loan, Determination of return on an investment, Determination of the value of a bond. Chapter 9 Problems 1. Future value (LO2) You invest $2,500 a year for three years at 8 percent. a . What is the value of your investment after one year? Multiply $2,500 × 1.08.
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