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Unformatted text preview: CHAPTER 5 The Time Value of Money Homework Solutions ANSWERS TO ENDOFCHAPTER QUESTIONS 51. The concept of time value of money is recognition that a dollar received today is worth more than a dollar received a year from now or at any future date. It exists because there are investment opportunities on money, that is, we can place our dollar received today in a savings account and one year from now have more than a dollar. 52. Compounding and discounting are inverse processes of each other. In compounding, money is moved forward in time, while in discounting money is moved back in time. This can be shown mathematically in the compounding equation: FV n = PV (1 + i) n We can derive the discounting equation by multiplying each side of this equation by and we get: PV = FV n 53. We know that FV n = PV(1 + i) n Thus, an increase in i will increase FV n and a decrease in n will decrease FV n. 54. Bank C which compounds daily pays the highest interest. This occurs because, while all banks pay the same interest, 5 percent, bank C compounds the 5 percent daily. Daily compounding allows interest to be earned more frequently than the other compounding periods. 55. The values in the present value of an annuity table (Table 58) are actually derived from the values in the present value table (Table 54). This can be seen, by examining the values represented in each table. The present value table gives values of for various values of i and n, while the present value of an annuity table gives 91 values of = + n 1 t t i) (1 1 for various values of i and n. Thus the value in the present value of annuity table for an nyear annuity for any discount rate i is merely the sum of the first n values in the present value table. PVIFA 10%,10yrs = 6.145. = 10 1 n PVIF10%,n = 6.144 = 0.909 + 0.826 + 0.751 + 0.683 + 0.621 + 0.564 + 0.513 + 0.467 + 0.424 + 0.386 56. An annuity is a series of equal dollar payments for a specified number of years. Examples of annuities include mortgage payments, interest payments on bonds, fixed lease payments, and any fixed contractual payment. A perpetuity is an annuity that continues forever, that is, every year from now on this investment pays the same dollar amount. The difference between an annuity and a perpetuity is that a perpetuity has no termination date whereas an annuity does. 92 SOLUTIONS TO ENDOFCHAPTER PROBLEMS Solutions to Problem Set A 51A. (a) FV 10 = $12,970 (b) FV 7 = $13,712 (c) FV 12 = $3,019.40 (d) FV 5 = $26,796.00 52A. (a) Thus n = 15 years (b) Thus, n = 5 years (c) Thus, n = 6 years (d) Thus, n = 20 years 53A. (a) Thus, i = 12 (b) Thus, i = 5% (c) Thus, i = 9% (d) Thus, i = 20% 54A. (a) PV = $308.80 (b) PV = $235.20 (c) PV = $789 (d) PV = $233 55A. (a) FV 10 = $6,289 (b) FV 5 = 610.50 (c) FV 7 = $302.89 (d) FV 3 = $76.50 56A. (a) PV = $17,560 (b) PV = $198.03 (c) PV = $1,562.96 (d) PV = $3,072.50 93 57A.57A....
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This note was uploaded on 02/20/2010 for the course FIN 565 taught by Professor Libnitz during the Spring '10 term at Academy of Design Tampa.
 Spring '10
 LIbnitz
 Finance, Time Value Of Money

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