I have a question and its answer. only one part of it is unclear. please only an

Question

I have a question and its answer. only one part of it is unclear. please only answer that part. you will see my explanation in below. I posted few pictures please read them and my comment to see where I have problem.

here is the question : ( for the sake opf time, let us only focus on suspension bridge)

I have problem with present value from gradient value ( 4% annual increase ). in solution, writer used below equation :

I cannot use that equation becasue we are not give that equation. instead I have below equation for gradient value

I know that i is 0.08 and n is 50 but here is how I calculated G. 2*0.04 = 0.08 ( 2 each year * percent of increase ) so when I put the number in above equation. I get 11.17 but in solution we have 42.43. please explain me why I am wrong and how can I calculate P value with above equation not in solution.

thanks

In order to improve evacuation routes Orleans in the event of another as Hurricane Katrina, the Louis Transportation (LDoT) is planning additional bridge across the Miss department uses an interest rate of gc Ver a 50-year life for either bridge. the better present worth? Contributec desig McCright, University of South Fl out of major disastet 5-33 In Co and uted SuspensionCantilever Bridge All Costs in $M Initial construction Land acquisition Annual O&M Bridge $585 120 $470 95 4% 185 Annual increase 0.3 210 Major maintena (Year 25) Salvage cost 30 27

Explanation / Answer

The problem lies in assuming Arithmetic Gradient whereas the question is of Geometric gradient and hence you would have to use the authr's formula..The formula you have used is for Arithmetic gradient.

In Arithmetic gradient, cash flows are 0,g,2g,3g....

In Geometric gradient, cash flows are 1,g,g^2,g^3....

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