Juan Garza invested $20,000 10 years ago at 12 percent, compounded quarterly How much has he accumulated? Solution: Appendix a FV=PVX FVIF(3%0, 40 periods) FV=$20,000X3.262=$65,240 9-20 Determine the amount of money in a savings account at the end of five years given an initial deposit of $5,000 and a 12 percent annual interest rate when interest is compounded (a)annually, (b) semiannually, and(c) quarterl Solution: Appendix a FV≡PVxFⅤIF a.$5000x1.762=$8,810(12%,5 periods) b.$5000X1.791=$8,955(6%,10 periods) c.$5000x1.806=$9030(3%,20 periods) 9-21 As stated in the chapter, the annuity payments are assumed to come at the end of each payment period(termed an ord inary annuity ) However, an exception occurs when the annuity payments come at the beginning of each period ( termed an annuity due). To find the present value of an annuity due, subtract 1 from n and add 1 to the tabular value. To find the future value of an annuity add 1 to n and subtract 1 from the tabular value. For example, to find the future value of a $100 payment at the beginning of each period for five periods at 10 percent, you would go to Appendix C for n=6 and i=10 percent. Look up the value of 7. 716 and subtract 1 from it for an answer of 6.716 or $671.60($100 X 6.716) What is the future value of a 10-year annuity of $4,000 per period where payments come at the beginning of each period The interest rate is 12 percent Solution: Appendix c FVAFAX FVIEA n=11.i=12%20.655-1=19655 FVA=$4,000×19655=$78620 -315 Copyright C2005 by The McGraw-Hill Companies, Inc
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-315 9-19. Juan Garza invested $20,000 10 years ago at 12 percent, compounded quarterly. How much has he accumulated? Solution: Appendix A FV = PV x FVIF (3%, 40 periods) FV = $20,000 x 3.262 = $65,240 9-20. Determine the amount of money in a savings account at the end of five years, given an initial deposit of $5,000 and a 12 percent annual interest rate when interest is compounded (a) annually, (b) semiannually, and (c) quarterly. Solution: Appendix A FV = PV x FVIF a. $5,000 x 1.762 = $8,810 (12%, 5 periods) b. $5,000 x 1.791 = $8,955 (6%, 10 periods) c. $5,000 x 1.806 = $9,030 (3%, 20 periods) 9-21. As stated in the chapter, the annuity payments are assumed to come at the end of each payment period (termed an ordinary annuity). However, an exception occurs when the annuity payments come at the beginning of each period (termed an annuity due). To find the present value of an annuity due, subtract 1 from n and add 1 to the tabular value. To find the future value of an annuity, add 1 to n and subtract 1 from the tabular value. For example, to find the future value of a $100 payment at the beginning of each period for five periods at 10 percent, you would go to Appendix C for n = 6 and i = 10 percent. Look up the value of 7.716 and subtract 1 from it for an answer of 6.716 or $671.60 ($100 x 6.716). What is the future value of a 10-year annuity of $4,000 per period where payments come at the beginning of each period. The interest rate is 12 percent. Solution: Appendix C FVA = A x FVIFA n = 11, i = 12% 20.655 – 1 = 19.655 FVA = $4,000 x 19.655 = $78,620
Your rich godfather has offered you a choice of one of the three following alternatives: $10,000 now; $2,000 a year for eight years; or $24,000 at the end of eight years. Assuming you could earn 1 l percent annually, which alternative should you choose? If you could earn 12 nt annually would you still choose the same alternative? Solution: (first alternative) Present value of $10,000 received now $10,000 (second alternative) Present value of annuity of $2,000 for eight years Appendix d PVA EAX PVIE =$2, 000X PVIFA (11%,8 years $2000x5.146 $10,292 (third alternative) Present value of $24,000 received in eight years dix B P=FⅤ X PIE =$24,000 X PVIF(11%,8 years) =$24000x.434 $10,416 Select $24,000 to be received in eight years by The McGraw-Hill Compa -316
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-316 9-22. Your rich godfather has offered you a choice of one of the three following alternatives: $10,000 now; $2,000 a year for eight years; or $24,000 at the end of eight years. Assuming you could earn 11 percent annually, which alternative should you choose? If you could earn 12 percent annually, would you still choose the same alternative? Solution: (first alternative) Present value of $10,000 received now: $10,000 (second alternative) Present value of annuity of $2,000 for eight years: Appendix D PVA = A x PVIFA = $2,000 x PVIFA (11%, 8 years) = $2,000 x 5.146 = $10,292 (third alternative) Present value of $24,000 received in eight years: Appendix B PV = FV x PVIF = $24,000 x PVIF (11%, 8 years) = $24,000 x .434 = $10,416 Select $24,000 to be received in eight years