EBK ENGINEERING FUNDAMENTALS: AN INTROD
EBK ENGINEERING FUNDAMENTALS: AN INTROD
5th Edition
ISBN: 9780100543409
Author: MOAVENI
Publisher: YUZU
Question
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Chapter 20, Problem 18P
To determine

Find the equivalent present worth, annual worth, and future worth of the cash flow diagram.

Expert Solution & Answer
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Answer to Problem 18P

The equivalent present worth, annual worth, and future worth of the cash flow diagram is $19150.55, $2853.43, and $41346.

Explanation of Solution

Given data:

The normal interest rate (i) is 8%.

Formula used:

Formula to calculate the present worth for the given cash flow diagram is,

PW=[$7000(PA,i,n)+$2000(PA,i,n)(PF,i,n)+$5000(PA,i,n)(PF,i,n)$7000(PF,i,n)] (1)

Here,

P is the present cost,

A is the uniform series payment,

F is the future cost,

i is the normal interest rate,

n is the number of years.

Refer the Problem 20.18 Figure in the textbook, the equation (1) is rewritten with respect to the given number of years is,

PW=[$7000(PA,i,5)+$2000(PA,i,5)(PF,i,2)+$5000(PA,i,2)(PF,i,7)$7000(PF,i,10)] (2)

Formula to calculate the present cost for the given uniform series payment is,

(PA,i,n)=[(1+i)n1i(1+i)n] (3)

Formula to calculate the present cost for the given future value is,

(PF,i,n)=1(1+i)n                                                                                                     (4)

Formula to calculate the annual worth for the given cash flow diagram is,

AW=PW(AP,i,n) (5)

Here,

PW is the present worth.

Refer the Problem 20.18 figure, the equation (5) is rewritten with respect to the given number of years is,

AW=PW(AP,i,10) (6)

Formula to calculate the uniform series payment for the given present cost is,

(AP,i,n)=[i(1+i)n(1+i)n1] (7)

Formula to calculate the future worth for the given cash flow diagram is,

FW=PW(FP,i,n) (8)

Refer the Problem 20.18 figure, the equation (8) is rewritten with respect to the given number of years is,

FW=PW(FP,i,10) (9)

Formula to calculate the future cost for the given present cost is,

(FP,i,n)=(1+i)n                                                                                                    (10)

Calculation:

Case (i): Equivalent present worth.

Substitute 8% for i, and 5 for n in equation (3) to find (PA,i,5).

(PA,i,5)=[(1+(8%))51(8%)(1+(8%))5]

(PA,i,5)=[(1+0.08)510.08(1+0.08)5]=3.993

Substitute 8% for i, and 2 for n in equation (4) to find (PF,i,2).

(PF,i,2)=1(1+(8%))2=1(1+0.08)2=0.857

Substitute 8% for i, and 2 for n in equation (3) to find (PA,i,2).

(PA,i,2)=[(1+(8%))21(8%)(1+(8%))2]=[(1+0.08)210.08(1+0.08)2]=1.783

Substitute 8% for i, and 7 for n in equation (4) to find (PF,i,7).

(PF,i,7)=1(1+(8%))7=1(1+0.08)7=0.583

Substitute 8% for i, and 10 for n in equation (4) to find (PF,i,10).

(PF,i,10)=1(1+(8%))10=1(1+0.08)10=0.463

Substitute 3.993 for (PA,i,5), 0.857 for (PF,i,2), 0.583 for (PF,i,7), 1.783 for (PA,i,2), and 0.463 for (PF,i,10) in equation (2) to find PW.

PW=$7000(3.993)+$2000(3.993)(0.857)+$5000(1.783)(0.583)$7000(0.463)=$19150.55

Case (ii): Equivalent annual worth.

Substitute 8% for i, and 10 for n in equation (7) to find (AP,i,10).

(AP,i,10)=[(8%)(1+(8%))10(1+(8%))101]=[0.08(1+0.08)10(1+0.08)101]=0.149

Substitute $19150.55 for PW, and 0.149 for (AP,i,10) in equation (6) to find AW.

AW=($19150.55)(0.149)=$2853.43

Case (iii): Equivalent future worth.

Substitute 8% for i, and 10 for n in equation (10) to find (FP,i,10).

(FP,i,10)=(1+(8%))10=(1+0.08)10=2.159

Substitute $19150.55 for PW, and 2.159 for (FP,i,10) in equation (9) to find FW.

FW=($19150.55)(2.159)=$41346

Therefore, the equivalent present worth, annual worth, and future worth of the cash flow diagram is $19150.55, $2853.43, and $41346.

Conclusion:

Thus, the equivalent present worth, annual worth, and future worth of the cash flow diagram is $19150.55, $2853.43, and $41346.

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