Chapter 10 Solution

# Given term 20 years j 48 compounded monthly pmt 1000

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Unformatted text preview: t required to fund each annuity is the present value of the annuity discounted at the interest rate the money can earn. For both annuities, PMT = \$200 monthly and i = 6% = 0.5% 12 For the 30-year annuity, 1 − ( 1 + i ) −n 1 − 1.005 − 360 = \$33,358.32 = \$200 PV = PMT 0.005 i For the 20-year annuity, PV = \$27,916.15. It requires \$33,358.32 – \$27,916.15 = \$5442.17 more to fund the extra 10 years. (This is only about 20% more money.) 52 Business Mathematics in Canada, 7/e Exercise 10.3 (continued) 19. The amount François and Pat must pay is the present value of all of the payments. The desired payment stream is equivalent to a succession of four 5-year annuities of: (i) \$2000 per quarter for the first 5 years, (ii) \$2500 per quarter for the next 5 years, (iii) \$3000 per quarter for the next 5 years, and (iv) \$3500 per quarter for the final 5 years. The present values of these annuities (at their respective beginnings) are: 1 − 1.0125− 20 (i) PV = \$2000 (ii) \$43,998.290 0.0125 = \$35,198.632; 1 − 1.0125− 20 (iii) PV = \$3000 0.0125 = \$52,797.948; (i) (ii) 5 I/Y P/Y 4 ENTER (making C/Y = P/Y = 4) 20 N 2000 PMT 0 FV CPT PV Ans: –35,198.632 \$35,198.632 + \$43,998.290 + 1.012520 \$52,797.948 + 1.012540 \$61,597.606 1.012560 (iv) \$61,597.606 (iv) Same I/Y, P/Y, C/Y Same N, FV 3000 PMT CPT PV Ans: –52,797.948 Same I/Y, P/Y, C/Y Same N, FV 2500 PMT CPT PV Ans: –43,998.290 (iii) Same I/Y, P/Y, C/Y Same N, FV 3500 PMT CPT PV Ans: –61,597.606 The present value today of these four amounts is Same I/Y, P/Y, C/Y 20 N 0 PMT 43998.290 FV CPT PV Ans: –34,319.042 Same I/Y, P/Y, C/Y 60 N 0 PMT 61597.606 FV CPT PV Ans: –29,232.228 Same I/Y, P/Y, C/Y 40 N 0 PMT 52797.948 FV CPT PV Ans: –32,122.976 = \$35,198.632 + \$34,319.042 + 32,122.976 + 29,232.254 = \$130,872.90 François and Pat must pay \$130,872.90. Exercise 10.3 (continued) 21. Original loan = Present value of all payments % Given: PMT = \$2000, n = 10, and i = 71 = 7% Chapter 10: Ordinary Annuities: Future Value and Present Value 7 I/Y P/Y 1 ENT...
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## This document was uploaded on 02/08/2014.

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