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Selected solutions 2
1.
Chapter 2 1 PROPRIETARY
MATERIAL. © The McGraw-Hill Companies, Inc. All rights reserved. No part of this solution may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to students, teachers and educators permitted by McGraw-Hill for their individual courses. As a student, you are invited to refer to and learn from this solution, but you should not submit it as your own work for a course in which you are enrolled. Such action is considered plagiarism. SOLUTIONS TO SELECTED PROBLEMS Student: You should work the problem completely before referring to the solution. CHAPTER 2 Solutions included for problems 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, and 82 2.1 1. (F/P,8%25) = 6.8485; 2. (P/A,3%,8) = 7.0197; 3. (P/G,9%,20) = 61.7770; 4. (F/A,15%,18) = 75.8364; 5. (A/P,30%,15) = 0.30598 2.4 P = 600,000(P/F,12%,4) = 600,000(0.6355) = $381,300 2.7 P = 75(P/F,18%,2) = 75(0.7182) = $53.865 million 2.10 P = 162,000(P/F,12%,6) = 162,000(0.5066) = $82,069 2.13 P = 1.25(0.10)(P/F,8%,2) + 0.5(0.10)(P/F,8%,5) = 0.125(0.8573) + 0.05(0.6806) = $141,193 2.16 A = 1.8(A/P,12%,6) = 1.8(0.24323) = $437,814 2.19 P = 75,000(P/A,15%,5) = 75,000(3.3522) = $251,415 2.22 P = 2000(P/A,8%,35) = 2000(11.6546) = $23,309 2.25 (a) 1. Interpolate between n = 32 and n = 34: 1/2 = x/0.0014 x = 0.0007
2.
Chapter 2 2 PROPRIETARY
MATERIAL. © The McGraw-Hill Companies, Inc. All rights reserved. No part of this solution may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to students, teachers and educators permitted by McGraw-Hill for their individual courses. As a student, you are invited to refer to and learn from this solution, but you should not submit it as your own work for a course in which you are enrolled. Such action is considered plagiarism. (P/F,18%,33) = 0.0050 – 0.0007 = 0.0043 2. Interpolate between n = 50 and n = 55: 4/5 = x/0.0654 x = 0.05232 (A/G,12%,54) = 8.1597 + 0.05232 = 8.2120 (b) 1. (P/F,18%,33) = 1/(1+0.18)33 = 0.0042 2. (A/G,12%,54) = {(1/0.12) – 54/[(1+0.12)54 –1} = 8.2143 2.28 (a) G = $5 million (b) CF6 = $6030 million (c) n = 12 2.31 (a) CF3 = 280,000 – 2(50,000) = $180,000 (b) A = 280,000 – 50,000(A/G,12%,5) = 280,000 – 50,000(1.7746) = $191,270 2.34 A = 14,000 + 1500(A/G,12%,4) = 14,000 + 1500(1.3589) = $16,038 2.37 50 = 6(P/A,12%,6) + G(P/G,12%,6) 50 = 6(4.1114) + G(8.9302) G = $2,836,622 2.40 For g = i, P = 60,000(0.1)[15/(1 + 0.04)] = $86,538 2.43 First find P and then convert to F: P = 2000{1 – [(1+0.10)7 /(1+0.15)7 }]}/(0.15 – 0.10) = 2000(5.3481) = $10,696 F = 10,696(F/P,15%,7) = 10,696(2.6600) = $28,452
3.
Chapter 2 3 PROPRIETARY
MATERIAL. © The McGraw-Hill Companies, Inc. All rights reserved. No part of this solution may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to students, teachers and educators permitted by McGraw-Hill for their individual courses. As a student, you are invited to refer to and learn from this solution, but you should not submit it as your own work for a course in which you are enrolled. Such action is considered plagiarism. 2.46 g = i: P = 1000[20/(1 + 0.10)] = 1000[18.1818] = $18,182 2.49 Simple: Total interest = (0.12)(15) = 180% Compound: 1.8 = (1 + i)15 i = 4.0% 2.52 1,000,000 = 600,000(F/P,i,5) (F/P,i,5) = 1.6667 i = 10.8% (Spreadsheet) 2.55 85,000 = 30,000(P/A,i,5) + 8,000(P/G,i,5) i = 38.9% (Spreadsheet) 2.58 2,000,000 = 100,000(P/A,5%,n) (P/A,5%,n) = 20.000 From 5% table, n is between 40 and 45 years; by spreadsheet, 42 > n > 41 Therefore, n = 41 years 2.61 10A = A(F/A,10%,n) (F/A,10%,n) = 10.000 From 10% table, n is between 7 and 8 years; therefore, n = 8 years 2.64 P = 61,000(P/F,6%,4) = 61,000(0.7921) = $48,318 Answer is (c) 2.67 109.355 = 7(P/A,i,25) (P/A,i,25) = 15.6221 From tables, i = 4% Answer is (a) 2.70 P = 8000(P/A,10%,10) + 500(P/G,10%,10) = 8000(6.1446) + 500(22.8913) = $60,602.45 Answer is (a) 2.73 F = 100,000(F/A,18%,5) = 100,000(7.1542) = $715,420 Answer is (c)
4.
Chapter 2 4 PROPRIETARY
MATERIAL. © The McGraw-Hill Companies, Inc. All rights reserved. No part of this solution may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to students, teachers and educators permitted by McGraw-Hill for their individual courses. As a student, you are invited to refer to and learn from this solution, but you should not submit it as your own work for a course in which you are enrolled. Such action is considered plagiarism. 2.76 A = 100,000(A/P,12%,5) = 100,000(0.27741) = $27,741 Answer is (b) 2.79 F = 10,000(F/P,12%,5) + 10,000(F/P,12%,3) + 10,000 = 10,000(1.7623) + 10,000(1.4049) + 10,000 = $41,672 Answer is (c) 2.82 60,000 = 15,000(P/A,18%,n) (P/A,18%,n) = 4.000 n is between 7 and 8 Answer is (b)
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