Chapter 10 Solution

Chapter 10 Solution - 10 Ordinary Annuities Future Value...

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10 Ordinary Annuities: Future Value and Present Value Exercise 10.2 1. Given: j = 8%; m = 1; term = 25 years i = 1 % 8 = 8%; n = 1(25) = 25 ( 29 - + = i i PMT FV n 1 1 = PMT - 08 . 0 1 08 . 1 25 = 73.105940 PMT ( a ) PMT = \$1000 ( b ) PMT = \$2000 ( c ) PMT = \$3000 FV = \$73,105.94 FV = \$146,211.88 FV = \$219,317.82 Chapter 10: Ordinary Annuities: Future Value and Present Value 41 Same I/Y, P/Y, C/Y Same N, PV 2000 + / – PMT CPT FV Ans : 146,211.88 Same I/Y, P/Y, C/Y Same N, PV 3000 + / – PMT CPT FV Ans : 219,317.82 8 I/Y P/Y 1 ENTER (making C/Y = P/Y = 1) 25 N 0 PV 1000 + / – PMT CPT FV Ans : 73,105.94

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Exercise 10.2 (continued) 3. a. Given: n = 20, PMT = \$1000, i = 9% ( 29 - + = i i PMT FV n 1 1 = \$1000 - 09 0 1 09 1 20 . . = \$51,160.12 Similarly, (b) i = 10% (c) i = 11% (d) i = 12% 5. Given: PMT = \$100, n = 4(5.5) = 22, i = 4 10 % = 2.5% ( 29 - + = i i PMT FV n 1 1 = \$100 - 025 0 1 025 1 22 . . = \$2886.29 42 Business Mathematics in Canada, 7/e 9 I/Y P/Y 1 ENTER (making C/Y = P/Y = 1) 20 N 0 PV 1000 + / – PMT CPT FV Ans : 51,160.12 Same P/Y, C/Y, N, PMT 10 I/Y CPT FV Ans : 57,275.00 Same P/Y, C/Y, N, PMT 11 I/Y CPT FV Ans : 64,202.83 Same P/Y, C/Y, N, PMT 12 I/Y CPT FV Ans : 72,052.44 10 I/Y P/Y 4 ENTER (making C/Y = P/Y = 4) 22 N 0 PV 100 + / – PMT CPT FV Ans : 2886.29
Exercise 10.2 (continued) 7. Given: PMT = \$2000, n = 2(12.5) = 25, i = 2 5 7 % . = 3.75% ( 29 - + = i i PMT FV n 1 1 = \$2000 - 00375 0 1 00375 1 25 . . = \$80,542.25 9. Given: PMT = \$700, n = 4(7.75) = 31, i = 4 9 % = 2.25% ( 29 - + = i i PMT FV n 1 1 = \$700 - 0225 0 1 0225 1 31 . . = \$30,901.26 Chapter 10: Ordinary Annuities: Future Value and Present Value 43 7.5 I/Y P/Y 2 ENTER (making C/Y = P/Y = 2) 25 N 0 PV 2000 + / – PMT CPT FV Ans : 80,542.25 9 I/Y P/Y 4 ENTER (making C/Y = P/Y = 4) 31 N 0 PV 700 + / – PMT CPT FV Ans : 30,901.26

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Exercise 10.2 (continued) 11. Given: PMT = \$1000, n = 1(3) = 3, i = 1 8 % = 8% ( 29 - + = i i PMT FV n 1 1 = \$1000 - 0.08 1 1.08 3 = \$3246.40 The future value after 3 years is \$3246.40. 13. Given: PMT = \$1000 every half year for 17 years. n = 2(17) = 34, i = 2 6.4% = 3.2% ( 29 - + = i i PMT FV n 1 1 = \$1000 - 0.032 1 1.032 34 = \$59,942.63 The client’s investments are worth \$59,942.63 today. 15. a. Given: PMT = \$500, n = 4(20) = 80, i = 4 8 % = 2% ( 29 - + = i i PMT FV n 1 1 = \$500 - 02 0 1 02 1 80 . . = \$96,885.98 b . If, instead, i = 4 10 % = 2.5% FV = \$500 - 025 0 1 025 1 80 . . = \$124,191.36 Exercise 10.2 (continued) 17. The amount 5 years from now will be the combined future value of the \$20,000 already saved and the annual \$5000 contributions. That is, ( 29 FV PV i n = + 1 + ( 29 - + i i PMT n 1 1 = \$20,000 ( 29 5 0725 1 . + \$5000 - 0725 0 1 0725 1 5 . . = \$28,380.27 + \$28,897.48 = \$57,277.75 44 Business Mathematics in Canada, 7/e 8 I/Y P/Y 1 ENTER (making C/Y = P/Y = 1) 3 N 0 PV 1000 + / – PMT CPT FV Ans : 3246.40 6.4 I/Y P/Y 2 ENTER (making C/Y = P/Y = 2) 34 N 0 PV 1000 + / – PMT CPT FV Ans : 59,942.63
Exercise 10.2 (continued) 19. For the first 2 years, PMT = \$1200, n = 2(4) = 8, i = 4 10 % = 2.5%. The future value after 2 years is ( 29 - + = i i PMT FV n 1 1 = \$1200 - 025 0 1 025 1 8 .

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