This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storagein a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.
2.6) $8,000( / ,8%,5) $8,000(0.6806) $5, 444.8P P F 2.7) F $20,000(F / P,10%,2) $20,000(1.21) $24,200 2.8)
x Alternative 1
$100P
x Alternative 2
P $120(P / F ,8%,2) $120(0.8573) $102.88
x Alternative 2 is preferred 2.9) (a) F $7,000(F / P,9%,8) $7,000(1.9926) $13,948.2
(b) F $1,250(F / P,4%,12) $1,250(1.6010) $2,001.25 (c) F $5,000(F / P,7%,31) $5,000(8.1451) $40,725.5 (d) F $20,000(F / P,6%,7) $20,000(1.5036) $30,072
2.10) (a) P $4,500(P / F ,7%,6) $4,500(0.6663) $2,998.35
(b) P $6,000(P / F ,8%,15) $6,000(0.3152) $1,891.2 (c) P $20,000(P / F ,9%,5) $20,000(0.6499) $12,998 (d) P $12,000(P / F ,10%,8) $12,000(0.4665) $5,598
This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storagein a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.
3
2.11) (a) P $6,000(P / F ,8%,5) $6,000(0.6806) $4,083.6 (b) F $15,000(F / P,8%,4) $15,000(1.3605) $20,407.5 2.12)
3 (1 0.07)
log 3 log 1.0716.24 years (or 17 years)
NF P PN
N
�
2.13)
x 2 (1 0.12
log 2 log 1.126.12 years
NF P PN
N
�
)
x Rule of 72:
72 /12 6 years 2.14)
P $35,000(P / F ,9%,4) � $10,000(P / F ,9%,2) $35,000(0.7084) � $10,000(0.8417) $33,211
2.15)
x Simple interest:
I iPN (0.1)($1,000)(3) $300
x Compound interest:
I P (1� i)N �1ª¬ º¼ $1,000 (1� .095)3 �1ª¬ º¼ $312.93
This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storagein a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.
This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storagein a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.
5
2.25) (a) F $5,000(F / A,6%,6) $5,000(6.9753) $34,876.5 (b) F $9,000(F / A,7.25%,9) $108,928.76 (c) F $12,000(F / A,8%,25) $12,000(73.1059) $877,270.8 (d) F $6,000(F / A,9.75%,10) $94,485.71 2.26) (a) A $15,000( A / F ,5%,13) $15,000(0.0565) $847.5
(b) A $20,000( A / F ,6%,8) $20,000(0.1010) $2,020 (c) A $5,000( A / F ,8%,25) $5,000(0.0137) $68.5 (d) A $4,000( A / F ,6.85%,8) $391.98
2.27)
� �
$35,000 $3,000( / ,6%, )( / ,6%, ) 11.6666
1 0.06 111.6666
0.06log(1.06) log(1.7)
9.11 years
N
F A NF A N
N
N
� �
�
2.28)
$10,000 A(F / A,7%,5)A $1,738.92
2.29)
F $500(1.1)10 � $1,000(1.1)8 � $1,000(1.1)6
�$1,000(1.1)4 � $1,000(1.1)2 � $1,000 $8,886.12
2.30) (a) A $15,000( A / P,8%,5) $15,000(0.2505) $3,757.5 (b) A $3,500( A / P,9.5%,4) $1,092.22 (c) A $8,000( A / P,11%,3) $8,000(0.4092) $3,273.6 (d) A $25,000( A / P,6%,20) $25,000(0.0872) $2,180 2.31)
This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storagein a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.
This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storagein a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.
7
2.37)
P $100(P / F ,8%,1) � $150(P / F ,8%,3)�$200(P / F ,8%,5) � $250(P / F ,8%,7)�$300(P / F ,8%,9) � $350(P / F ,8%,11) $793.83
2.38)
A $15,000 � $3,000( A / G,9%,10) $15,000 � $3,000(3.7978) $3,606.6
(b) Note that the oil price increases at the annual rate of 5% while the oil production decreases at the annual rate of 10%. Therefore, the annual revenue can be expressed as follows:
1 1
1
1
$30(1 0.05) 100,000(1 0.10)
$3,000,000(0.945)$3,000,000(1 0.055)
n nn
n
n
A � �
�
�
� �
�
This revenue series is equivalent to a decreasing geometric gradient series with g = -5.5%.
This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storagein a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.
This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storagein a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.
9
2
3
4
Period Withdrawal11 $3,00012 $3,000(1.06)13 $3,000(1.06)14 $3,000(1.06)15 $3,000(1.06)
Equivalent worth of the withdrawal series at period 10, using i = 8%:
P $3,000(P / A1,6%,8%,5)
ħħ $3,000 �1� 1� 0.06� �5 1� 0.08� ��5
0.08 � 0.06� �ħħ $13,383.92
Assuming that each deposit is made at the end of each year, the following equivalence must be hold:
$13,384 ( / ,8%,10)
14.4866$923.88
A F AA
A
(b) Equivalent present worth of the withdrawal series at 6%
15$3,000( / ,6%,6%,5) $3,000 $14,150.94
1 0.06P P A
�
$14,151 A(F / A,6%,10) 13.1808A
A $1,073.60
2.44)
P [$100(F / A,10%,8) � $50(F / A,10%,6)�$50(F / A,10%,4)](P / F ,10%,8) [$100(11.4359) � $50(7.7156)�$50(4.6410)](0.4665) $821.70
This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storagein a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.
10
2.46)
P(1.1) � $500 $300(P / F ,10%,2)�$300(P / F ,10%,3) � $800(P / F ,10%,4) $300(0.8264)�$300(0.7513) � $800(0.6830)
P $472.46
2.47)
Computing the equivalent worth at period 3 will require only two different types of interest factors.
This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storagein a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.
This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storagein a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.
This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storagein a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.
This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storagein a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.
14
x 2 2 3 4 5
$200 $150 $50 $200 $50(1 ) (1 ) (1 ) (1 ) (1 )
Pi i i i
� � � �� � � � � i
x and solving i with Excel Goal Seek function, P1 P2
14.96%i 2.62)
5
$35,000 $10,000( / , ,5)$10,000(1 )28.47%
F P ii
i
�
2.63) The equivalent future worth of the prize payment series at the end of
Year 20 (or beginning of Year 21) is
F1 $1,952,381(F / A,6%,20) $1,952,381(36.7856) $71,819,506.51
The equivalent future worth of the lottery receipts is
This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storagein a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.
15
The main question is whether or not the U.S. government will be able to invest the social security deposits at 9.4% interest over 60 years.
This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storagein a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.
