Engineering Economy: Present Worth of Projected Savings

[JJRKnights]

Homework Statement

Standby Power for water utility pumps and other electrical devices is provided by diesel-powered generators. As an Alternative, the utility can use natural gas to power generators, but it will be a few years before the gas is available at remote sites. The utility estimates that by switching to gas, it will save $25,912 per year, starting 3 years from now. at an interest rate of 10% per year, determine the present worth in year 0 of the projected savings that will occur in years 3 through 10.

Homework Equations

P = F(1/(1+i)^n)

The Attempt at a Solution

Drew out the timeline, and have a arrow up at t = 3 with value 25,912. With the interest rate of 10% a year, does it go up in value or down? Also how do I even solve this problem, my professor is horrible, in the notes he gives you nothing relevant to the problems he assigns. I honestly am surprised that he even gets paid to teach.

 

[KataKoniK]

Hello,

I would approach this problem by first identifying the relevant variables and organizing them in a timeline. The variables in this problem are the present worth (P), future worth (F), interest rate (i), and number of periods (n). The timeline should start at year 0, since that is the present time, and extend to year 10, since that is the last year of the projected savings.

Next, I would use the formula P = F(1/(1+i)^n) to calculate the present worth of the projected savings. In this case, the future worth (F) is $25,912, the interest rate (i) is 10% per year, and the number of periods (n) is 7 (since the savings start in year 3 and end in year 10).

Plugging these values into the formula, we get:
P = $25,912(1/(1+0.10)^7) = $25,912(0.5084) = $13,170.39

Therefore, the present worth in year 0 of the projected savings is $13,170.39.

To answer your question about the interest rate, in this case, the value goes down because we are discounting the future worth to its present value.

I hope this helps. Let me know if you have any further questions.