# Math Help - Present worth analysis

1. ## Present worth analysis

Im doing a PW analysis of two road paving options.....so if the one plan is 10 years and the other 15, I would have to take them both out to 30 years to compare.

if the initial cost for plan A is 500k, annual maint. = 35k, periodic surfacing = 350k, and the resurfacing interval is every 10 years....

im trying to figure how to set it up

PW =500,000 + 35,000(P/F,i,30) + ?

im not sure how to handle the resurfacing.....it should be once every 10 years....

not sure?

2. I'm not real certain what your "P" and "F" are. I'll just use your notation with faith.

If v = 1/(1+i),

$PW = 500 + 35(P/F,i,30) + 350(v^{10}+v^{20}+v^{30})$

Or, if $v10 = [1/(1+i)]^{10}$, and i10 = (1/v10)-1

$PW = 500 + 35(P/F,i,30) + 350(P/F,i10,3)$

Are you CERTAIN there is Annual Maintenance in a Resurfacing year?

3. The annaul maintence is every year and the resurfacing is once every 10 years.....

but I dont believe there would be annaul maintence in a resurfacing year.

The P/F notation is used when you are trying to Find P knowing F

(tables)

Finding Present worth, knowing the Future value....

so if you know P, the interest, and the number of years you can look on the table and just plug and chug....