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Unformatted text preview: ties: Future Value and Present Value 59 Exercise 10.4 (continued) 5. Given: PMT = $1500, i = 7.9%, n = 1(8) = 8, and PV = $6383.65 At a focal date at the end of the period of deferral, FV of $6383.65 = PV of ordinary annuity −8 d = $1500 1 − 1.079 $6383.65 (1.079 ) 0.079 = $8652.77 Using formula (9-2) to calculate d, $8652.77 FV ln ln PV = $6383.65 = 4.00 payment intervals d= ln (1.079 ) ln(1 + i ) The period of deferral is 4 years. 60 Business Mathematics in Canada, 7/e Exercise 10.4 (continued) 7. Given: PMT = $400, i = 9.75% = 0.8125%, n = 12(14) = 180, and PV = $33,173.03 12 At a focal date at the end of the period of deferral, FV of $33,173.03 = PV of ordinary annuity 1 − 1.008125 −180 d = $37,758.55 $33,173.03 (1.008125 ) = $400 0.008125 Using formula (9-2) to calculate d, $37,758.55 FV ln ln PV = $33,173.03 = 16.00 payment intervals d= ln(1 + i ) ln (1.008125 ) The period of deferral is 16 months or 1 year and 4 months. 9. Today's economic value of the future payments is their present value (discounted at the time value of money). Viewing the payments as a deferred ordinary simple annuity, PMT = $1500, n = 4(11) = 44, d = 4(5.75) = 23, and i = 6.5% = 1.625% 4 1 − (1 + i ) − n PV(5.75 years from now) = PMT i = $1500 1 − 1.01625 −44 0.01625 = $46,891.229 PV(today) = FV (1 + i ) − d 6.5 I/Y P/Y 4 ENTER (making C/Y = P/Y = 4) 44 N 1500 PMT 0 FV CPT PV Ans: −46,891.229 Same I/Y, P/Y, C/Y 23 N 0 PMT 46891.229 FV CPT PV Ans: −32,365.24 = $46,891.229 (1.01625 ) −23 = $32,365.24 Chapter 10: Ordinary Annuities: Future Value and Present Value 61 Exercise 10.4 (continued) 11. Today’s economic value economic is the present value. For the $1000 annuity, 1 − (1 + i ) − n PV(today) = PMT i 1 − 1.065 − 10 = $1000 0.065 = $7188.83 For the $2000 annuity, PV(10 years from now) 1 − 1.065 −10 = $2000 0.065 = $14,377.66 PV(today) = $14,377.66 1.065 10 6.5 I/Y P/Y 1 ENTER (making C/Y = P/Y = 1) 10 N 1000 PMT 0 FV CPT PV Ans: −7188.83 Same I/Y, P/Y, C/Y Same N, FV 2000 PMT CPT PV Ans: −14,377.66 = Same I/Y, P/Y, C/Y, N 0 PMT 1...
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This document was uploaded on 02/08/2014.

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