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Unformatted text preview: ,590.13 1 − (1 + i ) − n 2 PV(4.25 yrs. from now) = PMT i2 1 − 1.01507512 5 − 80 = $2000 0.01507512 5 = $92,590.13 (continued) 76 Business Mathematics in Canada, 7/e Exercise 10.5 (continued) 35. (continued) Same I/Y, P/Y, C/Y 17 N 0 PMT 92590.13 FV CPT PV Ans: −71,795.22 PV(today) = FV (1 + i ) − d = $92,590.13 (1.015075125 ) − 17 = $71,795 (to the nearest dollar) % 37. Given: PMT = $356.83; i = 74 = 1.75%; c = 4 12 = 0.3 ; n = 12(12.5) = 150; PV = $30,000 i2 = (1 + i ) c − 1 = (1.0175 ) 0. 3 – 1 = 0.005799633 At a focal date at the end of the period of deferral, FV of $30,000 loan = PV of loan payments 1 − 1.0057996326 −150 Right hand side = $356.83 0.0057996326 = $35,683.49 Left hand side = $30,000 (1.0057996326) d Hence, $30,000 (1.0057996326 ) d = $35,683.49 Using formula (9-2) to calculate d, $35,683.49 FV ln ln $30,000 = 30.00 PV = d= ln (1.00579963 26 ) ln(1 + i ) The period of deferral is 30 payment intervals, that is, 30 months or 2 years and 6 months. Chapter 10: Ordinary Annuities: Future Value and Present Value 7 I/Y P/Y 12 ENTER C/Y 4 ENTER 150 N 356.83 PMT 0 FV CPT PV Ans: –35,683.49 Same I/Y, P/Y, C/Y 30000 + / – PV 0 PMT 35683.49 FV CPT N Ans: 30.00 77 Exercise 10.5 (continued) 39. The initial investment equals the present value of the withdrawals. Given: PV = $19,665, PMT = $1000, n = 60, i = 9.5% = 4.75%, and c = 2 =0.5. 2 4 i2 = (1 + i ) c − 1 = (1.0475 ) 0.5 – 1 = 0.023474475 With the focal date at the end of the period of deferral, FV of $19,665 = PV of ordinary annuity 1 − 1.02347447 5 −60 = Right hand side = $1000 0.02347447 5 $32,012.21 Left hand side = $19,665 (1.0475 ) d Hence, $19,665 (1.0475 ) d = $32,012.21 Using formula (9-2) to calculate d, $32,012.21 FV ln ln $19,665 = 21.00 PV = d= ln (1.02347447 5 ) ln(1 + i ) The period of deferral is 21 quarters long. The investment must be made 22 quarters or 5 years and 6 months before the first withdrawal. 9.5 I/Y P/Y 4 ENTER C/Y 2 ENTER 60 N 1000 PMT 0 FV CPT PV Ans...
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