Chapter 10 Solution

# 229 same iy py cy 23 n 0 pmt 46891229 fv cpt pv ans

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Unformatted text preview: 4377.66 FV CPT PV Ans: −7659.35 \$7659.35 The \$2000 annuity has the greater (by \$470.52) economic value. 62 Business Mathematics in Canada, 7/e Exercise 10.4 (continued) 13. The price paid will be the present value of the payments discounted at the required rate of return. Since the first payment is due in 6 months, the period of deferral is 5 months (in order to treat the payments as a deferred ordinary annuity). 18 I/Y P/Y 12 ENTER % Given: PMT = \$231, n = 15, d = 5, and i = 182 = (making C/Y = P/Y = 12) 1 1.5% 15 N 231 PMT 1 − (1 + i ) − n 0 FV PV(5 months from now) = PMT i CPT PV Ans: –3082.287 1 − 1.015 −15 = \$231 0.015 = \$3082.287 PV(today) = FV (1 + i ) − d = \$3082.29 (1.015 ) −5 = \$2861.16 The finance company will pay \$2861.16 for the contract. Same I/Y, P/Y, C/Y 5 N 0 PMT 3082.287 FV CPT PV Ans: −2861.16 15. The original loan equals the present value of the payments. Thus, PV = \$35,000 with PMT = \$1573.83, n = 4(12) = 48, and i = 10% = 2.5%. 4 At a focal date at the end of the period of deferral, FV of \$35,000 = PV of ordinary annuity 1 − 1.025 −48 = \$43,710.22 \$35,000 (1.025 ) d = \$1573.83 0.025 Using formula (9-2) to calculate d, \$43,710.22 FV ln ln PV = \$35,000 = 9.00 d= ln(1 + i ) ln (1.025 ) The period of deferral was 9 quarters long. The interval between the date of the loan and the first payment was 10 quarters or 2 years and 6 months. Exercise 10.4 (continued) 17. Given: For the initial investment, PV = \$10,000, i = 8.5% = 4.25%. 2 For the deferred annuity, PMT = \$1000, n = 40, and i = 4.25%. At a focal date at the end of the period of deferral, 8.5 I/Y FV of \$10,000 = PV of ordinary annuity P/Y 2 ENTER −40 d = \$1000 1 − 1.0425 (making C/Y = P/Y = 2) \$10,000 (1.0425 ) 0.0425 40 N 1000 PMT = \$19,077.27 0 FV Chapter 10: Ordinary Annuities: Future Value and Present Value CPT PV 63 Ans: –19,077.27 Using formula (9-2) to calculate d, \$19,077.27 FV ln ln PV = \$10,000 = 15.52 d= ln(1 + i ) ln (1.0425 ) The period of deferral is 15.52 half years o...
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