Finance geometric gradient determine present worth

J

Jill

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Can some please let me know if my calcutations are correct ASAP?

This is th problem: The Engineering Economics Finance Company (EEFC) plans to receive $990,000 next year from a certain investment, with increases of 5% per year. If N = 4 years and the interest rate is 10%, determine the present worth of the cash flows.

Here is my solution: This is a geometric gradient
Formula: A(1-(1+g)^n (1+i)^-n/(i-g)

990,000(1-(1.05)^4 (1+.10)^-4/.10-.05

990,000(1-(1.21550625)(.6830134554)/.05

990,000(1-(.8302071239)/.05
990,000(.1697928671/.05
990,000(3.395857523)=3361898.95

Is my calculation and answer correct?

Thanks, Jill
 
Oh my goodness I actually am learning something :D . Thank You Very Much!!! I do have some more to post, please bear with me I just want to make sure I am doing them correctly.
 
Another way to look at it:
[990000(1.05)^0 / 1.10^1] + [990000(1.05)^1 / 1.10^2] + [990000(1.05)^2 / 1.10^3] + [990000(1.05)^3 / 1.10^4]
= 3,361,898.95
 
Denise,

Isn't this just a find the Present Value of a series of equal cash flow, why do they make these so difficult as far a using the geometric gradient? In the end both formulas work out to be the same result.
 
Not quite; the cash flows here are not equal, since they increase by 5%.

IF the 5% didn't apply, then the formula would represent the sum of these:
[990000 / 1.10^1] + [990000 / 1.10^2] + [990000 / 1.10^3] + [990000 / 1.10^4]

The formula being: f(1 - x) / i where x = 1/(1+i)^n : 990000(1-x) / .10 where x = 1/(1.10)^4
 
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