Each year you need to power wash your deck. You can rent a power washer for $38 per day. If you go with this option, you will pay $38 each year starting today up to and including year 10 If you buy the power washer, you will pay $175 today and the power washer will last up to and including year 10. If your investments earn 4% compounded annually, how much does it save you in present value terms to own the power washer

You will save $133.21 by buying the washer.

Explanation:

Giving the following information:

Rent = $38 per day.

Number of years = 10 years

Buying price = $175

I will assume that you rent the washer one day each year.

First, we need to calculate the final value of renting the washer.

FV = {A*[ (1+i) ^n-1]}/i

A = annual pay = 38

i = 0.04

n = 10

FV = {38*[ (1.04^10) - 1]} / 0.04 = 456.23

Now, we can calculate the present value:

PV = FV / (1+i) ^n

PV = 456.23 / 1.04^10 = $308.21

You will save (308.21-175) $133.21 by buying the washer.