Factors: How Time and Interest Affect Money

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- (a) G = $5 million (b) CF6 = $6030 million (c) n = 12

- (a) G = $100 (b) CF5 = 900 – 100(5) = $400

2.30 300,000 = A + 10,000(A/G,10%,5)

300,000 = A + 10,000(1.8101)

A = $281,899

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

- (a) CF3 = 4000 + 2(1000)

= $6000

(b) P = 4000(P/A,10%,5) + 1000(P/G,10%,5)

= 4000(3.7908) + 1000(6.8618)

= $22,025

- P = 150,000(P/A,15%,8) + 10,000(P/G,15%,8)

= 150,000(4.4873) + 10,000(12.4807)

= $797,902

- A = 14,000 + 1500(A/G,12%,5)

= 14,000 + 1500(1.7746)

= $16,662

- (a) Cost = 2000/0.2

= $10,000

(b) A = 2000 + 250(A/G,18%,5)

= 2000 + 250(1.6728)

= $2418

- Convert future to present and then solve for G using P/G factor:

6000(P/F,15%,4) = 2000(P/A,15%,4) – G(P/G,15%,4)

6000(0.5718) = 2000(2.8550) – G(3.7864)

G = $601.94

- 50 = 6(P/A,12%,6) + G(P/G,12%,6)

50 = 6(4.1114) + G(8.9302)

G = $2,836,622

- A = [4 + 0.5(A/G,16%,5)] – [1 –0.1(A/G,16%,5)

= [4 + 0.5(1.7060)] – [1 –0.1(1.7060)]

= $4,023,600

- For n = 1: {1 – [(1+0.04)1/(1+0.10)1}]}/(0.10 –0.04) = 0.9091

For n = 2: {1 – [(1+0.04)2/(1+0.10)2}]}/(0.10 –0.04) = 1.7686

For n = 3: {1 – [(1+0.04)3/(1+0.10)3}]}/(0.10 –0.04) = 2.5812

- For g = i, P = 60,000(0.1)[15/(1 + 0.04)]

= $86,538

- P = 25,000{1 – [(1+0.06)3/(1+0.15)3}]}/(0.15 – 0.06)

= $60,247

- Find P and then convert to A.

P = 5,000,000(0.01){1 – [(1+0.20)5/(1+0.10)5}]}/(0.10 – 0.20)

= 50,000{5.4505}

= $272,525

A = 272,525(A/P,10%,5)

= 272,525(0.26380)

= $71,892

- 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

- First convert future worth to P, then use Pg equation to find A.

P = 80,000(P/F,15%,10)

= 80,000(0.2472)

= $19,776

19,776 = A{1 – [(1+0.09)10/(1+0.15)10}]}/(0.15 – 0.09)

19,776 = A{6.9137}

A = $2860

- Find A in year 1 and then find next value.

900,000 = A{1 – [(1+0.05)5/(1+0.15)5}]}/(0.15 – 0.05)

900,000 = A{3.6546)

A = $246,263 in year 1

Cost in year 2 = 246,263(1.05)

= $258,576

- g = i: P = 1000[20/(1 + 0.10)]

= 1000[18.1818]

= $18,182

- Find P and then convert to F.

P = 3000{1 – [(1+0.05)4/(1+0.08)4}]}/(0.08 –0.05)

= 3000{3.5522}

= $10,657

F = 10,657(F/P,8%,4)

= 10,657(1.3605)

= $14,498

2.48 Decrease deposit in year 4 by 5% per year for three years to get back to year 1.

First deposit = 1250/(1 + 0.05)3

= $1079.80

- Simple: Total interest = (0.12)(15) = 180%

Compound: 1.8 = (1 + i)15

i = 4.0%

- Profit/year = 6(3000)/0.05 = $360,000

1,200,000 = 360,000(P/A,i,10)

(P/A,i,10) = 3.3333

i = 27.3% (Excel)

- 2,400,000 = 760,000(P/A,i,5)

(P/A,i,5) = 3.15789

i = 17.6% (Excel)

- 1,000,000 = 600,000(F/P,i,5)

(F/P,i,5) = 1.6667

i = 10.8%