Ing.economica

Chapter 3

Combining Factors

Solutions to Problems

3.1 P = 100,000(260)(P/A,10%,8)(P/F,10%,2)

= 26,000,000(5.3349)(0.8264)

= $114.628 million

3.2 P = 50,000(56)(P/A,8%,4)(P/F,8%,1)

= 2,800,000(3.3121)(0.9259)

= $8.587 million

3.3 P = 80(2000)(P/A,18%,3) + 100(2500)(P/A,18%,5)(P/F,18%,3)

= 160,000(2.1743) + 250,000(3.1272)(0.6086)

= $823,691

3.4 P = 100,000(P/A,15%,3) + 200,000(P/A,15%,2)(P/F,15%,3)

= 100,000(2.2832) + 200,000(1.6257)(0.6575)

= $442,100

3.5 P = 150,000 + 150,000(P/A,10%,5)

= 150,000 + 150,000(3.7908)

= $718,620

3.6 P = 3500(P/A,10%,3) + 5000(P/A,10%,7)(P/F,10%,3)

= 3500(2.4869) + 5000(4.8684)(0.7513)

= $26,992

3.7 A = [0.701(5.4)(P/A,20%,2) + 0.701(6.1)(P/A,20%,2)((P/F,20%,2)](A/P,20%,4)

= [3.7854(1.5278) + 4.2761(1.5278)(0.6944)](0.38629)

= $3.986 billion

3.8 A = 4000 + 1000(F/A,10%,4)(A/F,10%,7)

= 4000 + 1000(4.6410)(0.10541)

= $4489.21

3.9 A = 20,000(P/A,8%,4)(A/F,8%,14)

= 20,000(3.3121)(0.04130)

= $2735.79

3.10 A = 8000(A/P,10%,10) + 600

= 8000(0.16275) + 600

= $1902

3.11 A = 20,000(F/P,8%,1)(A/P,8%,8)

= 20,000(1.08)(0.17401)

= $3758.62

3.12 A = 10,000(F/A,8%,26)(A/P,8%,30)

= 10,000(79.9544)(0.08883)

= $71,023

3.13 A = 15,000(F/A,8%,9)(A/F,8%,10)

= 15,000(12.4876)(0.06903)

= $12,930

3.14 A = 80,000(A/P,10%,5) + 80,000

= 80,000(0.26380) + 80,000

= $101,104

3.15 A = 5000(A/P,6%,5) + 1,000,000(0.15)(0.75)

= 5000(0.2374) + 112,500

= $113,687

3.16 A = [20,000(F/A,8%,11) + 8000(F/A,8%,7)](A/F,8%,10)

= [20,000(16.6455) + 8000(8.9228)]{0.06903)

= $27,908

3.17 A = 600(A/P,12%,5) + 4000(P/A,12%,4)(A/P,12%,5)

= 600(0.27741) + 4000(3.0373)(0.27741)

= $3536.76

3.18 F = 10,000(F/A,15%,21)

= 10,000(118.8101)

= $1,188,101

3.19 100,000 = A(F/A,7%,5)(F/P,7%,10)

100,000 = A(5.7507)(1.9672)

A = $8839.56

3.20 F = 9000(F/P,8%,11) + 600(F/A,8%,11) + 100(F/A,8%,5)

= 9000(2.3316) + 600(16.6455) + 100(5.8666)

= $31,558

3.21 Worth in year 5 = -9000(F/P,12%,5) + 3000(P/A,12%,9)

= -9000(1.7623) + 3000(5.3282)

= $123.90

3.22 Amt, year 5 = 1000(F/A,12%,4)(F/P,12%,2) + 2000(P/A,12%,7)(P/F,12%,1)

= 1000(4.7793)(1.2544) + 2000(4.5638)(0.8929)

= $14,145

3.23 A = [10,000(F/P,12%,3) + 25,000](A/P,12%,7)

= [10,000(1.4049) + 25,000](0.21912)

= $8556.42

3.24 Cost of the ranch is P = 500(3000) = $1,500,000.

1,500,000 = x + 2x(P/F,8%,3)

1,500,000 = x + 2x(0.7938)

x = $579,688

3.25 Move unknown deposits to year –1, amortize using A/P, and set equal to $10,000.

x(F/A,10%,2)(F/P,10%,19)(A/P,10%,15) = 10,000

x(2.1000)(6.1159)(0.13147) = 10,000

x = $5922.34

3.26 350,000(P/F,15%,3) = 20,000(F/A,15%,5) + x

350,000(0.6575) = 20,000(6.7424) + x

x = $95,277

3.27 Move all cash flows to year 9.

0 = -800(F/A,14%,2)(F/P,14%,8) + 700(F/P,14%,7) + 700(F/P,14%,4)

–950(F/A,14%,2)(F/P,14%,1) + x – 800(P/A,14%,3)

0 = -800(2.14)2.8526) + 700(2.5023) + 700(1.6890)

–950(2.14)(1.14) + x – 800(2.3216)

x = $6124.64

3.28 Find P at t = 0 and then convert to A.

P = 5000 + 5000(P/A,12%,3) + 3000(P/A,12%,3)(P/F,12%,3)

+ 1000(P/A,12%,2)(P/F,12%,6)

= 5000 + 5000(2.4018) + 3000(2.4018)(0.7118)

+ 1000(1.6901)(0.5066)

= $22,994

A = 22,994(A/P,12%,8)

= 22,994(0.20130)

= $4628.69

3.29 F = 2500(F/A,12%,8)(F/P,12%,1) – 1000(F/A,12%,3)(F/P,12%,2)

= 2500(12.2997)(1.12) – 1000(3.3744)(1.2544)

= $30,206

3.30 15,000 = 2000 + 2000(P/A,15%,3) + 1000(P/A,15%,3)(P/F,15%,3) + x(P/F,15%,7)

15,000 = 2000 + 2000(2.2832) + 1000(2.2832)(0.6575) + x(0.3759)

x = $18,442

3.31 Amt, year 3 = 900(F/A,16%,4) + 3000(P/A,16%,2) – 1500(P/F,16%,3)

+ 500(P/A,16%,2)(P/F,16%,3)

= 900(5.0665) + 3000(1.6052) – 1500(0.6407)

+ 500(1.6052)(0.6407)

= $8928.63

3.32 A = 5000(A/P,12%,7) + 3500 + 1500(F/A,12%,4)(A/F,12%,7)

= 5000(0.21912) + 3500 + 1500(4.7793)(0.09912)

= $5306.19

3.33 20,000 = 2000(F/A,15%,2)(F/P,15%,7) + x(F/A,15%,7) + 1000(P/A,15%,3)

20,000 = 2000(2.1500)(2.6600) + x(11.0668) + 1000(2.2832)

x = $567.35

3.34 P = [4,100,000(P/A,6%,22) – 50,000(P/G,6%,22)](P/F,6%,3)

+ 4,100,000(P/A,6%,3)

= [4,100,000(12.0416) – 50,000(98.9412](0.8396)

+ 4,100,000(2.6730)

= $48,257,271

3.35 P = [2,800,000(P/A,12%,7) + 100,000(P/G,12%,7) + 2,800,000](P/F,12%,1)

= [2,800,000(4.5638) + 100,000(11.6443) + 2,800,000](0.8929)

= $14,949,887

3.36 P for maintenance = [11,500(F/A,10%,2) + 11,500(P/A,10%,8)

+ 1000(P/G,10%,8)](P/F,10%,2)

= [11,500(2.10) + 11,500(5.3349)

...