Question

6.13Nicole and Amy share an apartment and work at H20 Engineering, and they have decided to Ov Pure drink more water each day. The recommended amount is eight 8-ounce glasses, or 64 ounces, per Sa day. This is a total of one gallon per day for the Ex two of them. Using this 1 gallon (or 3.78 liters- equivalent) basis for three possible sources of drinking water, determine the monthly cost and present worth value for one year of use. For each source, the average cost and amount of source wa- ter estimated to be used to get a gallon of drinking water is tabulated. Let i = 6% per year com- pounded monthly and assume 30 days per month. Gallons used per Average Cost Gallon Drank Method Bottles from store shelf in-home filtration | system Tap water $1 per gallon Sa 27c per gallon $2.75 per 1000 gallons

Answer 1

Monthly (nominal) interest rate = 6%/12 = 0.5%

Number of months = 12

(i) Bottles from store shelf

Monthly cost = $1 x 1 x 30 = $30

Present value ($) = 30 x P/A(0.5%, 12) = 30 x 11.6189** = 348.57

(ii) In-home filtration

Monthly cost = $0.27 x 2 x 30 = $16.2

Present value ($) = 16.2 x P/A(0.5%, 12) = 16.2 x 11.6189** = 188.23

(iii) Tap water

Monthly cost = $2.75 x (5/1000) x 30 = $0.4125

Present value ($) = 0.4125 x P/A(0.5%, 12) = 0.4125 x 11.6189** = 4.79

**P/A(r%, N) = [1 - (1 + r)^-N] / r

P/A(0.5%, 12) = [1 - (1.005)^-12] / 0.005 = (1 - 0.9419) / 0.005 = 0.0581 / 0.005 = 11.6189