EBK ENGINEERING FUNDAMENTALS: AN INTROD
EBK ENGINEERING FUNDAMENTALS: AN INTROD
5th Edition
ISBN: 9780100543409
Author: MOAVENI
Publisher: YUZU
Question
Book Icon
Chapter 20, Problem 17P
To determine

Find the equivalent annual worth of the cash flow diagram.

Expert Solution & Answer
Check Mark

Answer to Problem 17P

The equivalent annual worth of the cash flow diagram is $3868.37.

Explanation of Solution

Given data:

The normal interest rate (i) is 8%.

Formula used:

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

AW=[$5000(PA,i,n)(AP,i,n)$2000(PA,i,n)(PF,i,n)(AP,i,n)+$8000(PF,i,n)(AP,i,n)+$5000(AF,i,n)] (1)

Here,

F is the future cost,

P is the present cost,

A is the uniform series payment,

i is the normal interest rate, and

n is the number of years.

Refer the Problem 20.17 Figure in the textbook, the equation (1) is rewritten with respect to the given number of years is,

AW=[$5000(PA,i,6)(AP,i,10)$2000(PA,i,3)(PF,i,4)(AP,i,10)+$8000(PF,i,8)(AP,i,10)+$5000(AF,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 uniform series payment for the given present cost is,

(AP,i,n)=[i(1+i)n(1+i)n1] (4)

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

(PF,i,n)=[1(1+i)n] (5)

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

(AF,i,n)=[i(1+i)n1] (6)

Calculation:

To calculate the equivalent annual worth of the cash flow diagram:

Substitute 8% for i, and 6 for n in equation (3) to find (PA,i,6).

(PA,i,6)=[(1+(8%))61(8%)(1+(8%))6]=[(1+0.08)610.08(1+0.08)6]=4.623

Substitute 8% for i, and 10 for n in equation (4) 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 8% for i, and 3 for n in equation (3) to find (PA,i,3).

(PA,i,3)=[(1+(8%))31(8%)(1+(8%))3]

(PA,i,3)=[(1+0.08)310.08(1+0.08)3]=2.577

Substitute 8% for i, and 4 for n in equation (5) to find (PF,i,4).

(PF,i,4)=[1(1+(8%))4]=[1(1+0.08)4]=0.735

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

(PF,i,8)=[1(1+(8%))8]=[1(1+0.08)8]=0.540

Substitute 8% for i, and 10 for n in equation (6) to find (AF,i,10).

(AF,i,10)=[(8%)(1+(8%))101]=[0.08(1+0.08)101]=0.069

Substitute 4.623 for (PA,i,6), 0.149 for (AP,i,10), 2.577 for (PA,i,3), 0.735 for (PF,i,4), 0.540 for (PF,i,8), and 0.069 for (AF,i,10) in equation (2) to find AW.

AW=[$5000(4.623)(0.149)$2000(2.577)(0.735)(0.149)+$8000(0.540)(0.149)+$5000(0.069)]=$3868.37

Therefore, the equivalent annual worth of the cash flow diagram is $3868.37.

Conclusion:

Thus, the equivalent annual worth of the cash flow diagram is $3868.37.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
*13-12. The control linkage for a machine consists of two L2 steel rods BE and FG, each with a diameter of 1 in. If a device at G causes the end G to freeze up and become pin connected, determine the maximum horizontal force P that could be applied to the handle without causing either of the two rods to buckle. The members are pin connected at A, B, D, E, and F. P 12 in. C G F B 2 in. E 4 in. 4 in. A D + -15 in.- + -20 in.-
13-31. The steel bar AB has a rectangular cross section. If it is pin connected at its ends, determine the maximum allowable intensity w of the distributed load that can be applied to BC without causing bar AB to buckle. Use a factor of safety with respect to buckling of 1.5. Est = 200 GPa, σy 360 MPa. = B W 5 m 3 m -20 mm 30 mm x x A 20 mm y C
Problem 1: A man-made 30 ft tall, 1.5:1 slope is to be build as shown in the figure. The soil is homogeneous with shear strength parameters c = 400 psf and φ = 290 . The moist unit weight of the soil is 119 pcf above the groundwater table and the saturated unit weight is 123 pcf below. Using the ordinary method of slices, compute the Factor of Safety (FS) along the trial failure surface shown. (Hint: Please note the unit weight is changing within the same slice.) Note 1: Use the same number of slices and dimensions as provided. Document ALL the calculations of weight (W) for each slice. Note 2: Document your solutions by following the same approach illustrated in the class, including a summary table showing all the variables and calculations involved in assessing FS.
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Engineering Fundamentals: An Introduction to Engi...
Civil Engineering
ISBN:9781305084766
Author:Saeed Moaveni
Publisher:Cengage Learning
Text book image
Fundamentals Of Construction Estimating
Civil Engineering
ISBN:9781337399395
Author:Pratt, David J.
Publisher:Cengage,
Text book image
Sustainable Energy
Civil Engineering
ISBN:9781337551663
Author:DUNLAP, Richard A.
Publisher:Cengage,
Text book image
Traffic and Highway Engineering
Civil Engineering
ISBN:9781305156241
Author:Garber, Nicholas J.
Publisher:Cengage Learning