The Cost of Installing a Home Water Filter

Not all of us are lucky enough to live in the Pacific Northwest, or get great water from natural springs like Enumclaw. What if you don't like the taste? Maybe you're concerned with contaminants, or the pipes in your home are getting old, or your body is more sensitive to additives in water (some doctors are prescribing bottled water, which as you will see is ridiculous), or maybe fluoride and chlorine just aren't your thing. Say you buy cases upon cases of bottled water, or even subscribe to a water cooler delivery service, because you can't stand tap. At the store it may seem like a good deal to buy a case of 24 for only $4.99 (especially when one is being sold for around $1.00), or get a blue five gallon jug delivered to your home or business for only $8.99. The question is: at what point does purchasing an under-the-sink water filtration system (reverse osmosis removes chlorine and fluoride) pay off? (When only considering cost. If you considered health effects, environmental effects, etc. it would "pay off" more quickly.)

I did do some math to get there, if you're uninterested in that process jump to the end to catch the answer to your question. 

First, let's go over the assumptions I made:
1. I'm assuming that your tap water costs $1.95 per CCF (100 cubic feet), the is the rate for the city of Enumclaw, if you're not in Enumclaw it's likely that your rate is equivalent or lower than this one.
2. I'm assuming that you really don't like tap water (as is the case for people who aren't supposed to drink it at all), meaning that most of your consumption is purchased water. I compared drinking 80 ounces of tap water to 80 ounces of bottled water, which is roughly equivalent to your recommended  daily intake of water, adjusted according to WebMD for modern humans (chances are that you're not running around all day) who get 20% of their daily water needs from the food you eat ("approximately 9 cups for women and 12.5 cups for men" I used 10 cups). This is equivalent to 4.7 16.9 ounce bottles a day (which doesn't seem practical, which is why I included water cooler and 24 pack cost).
It's very possible (and in fact almost always the case) that you don't just drink water, or like most of the population don't drink enough water. Juice, soda, or whatever will also contribute to your "water" intake, however it's impossible to calculate how much juice you're drinking etc., these are just general calculations which will give you an idea to how expensive bottled water can be.

I used three price points for bottled water, and in parenthesis is their respective cost for 80 ounces per day:
1. Expensive one bottle purchases (Pepsi and Coca-Cola brands): $1.79 per 16.9 oz bottle ($8.47 per day)
2. Moderately priced one bottle purchases: $1.00 per 16.9 oz bottle, a price is typical of vending machines ($4.73 per day)
3. Cheap one bottle purchases: $0.69 per 16.9 oz bottle ($3.26 per day)
4. 24 pack purchases: $4.99 per 24 pack ($0.98 per day)
5. Blue cooler purchases: $8.99 per five gallon water cooler from a common delivery service with a one-time ~$3 fee for a cooler stand ($1.12 per day)

I compared these to tap water ($0.0016 per day at 80 ounces) with the cost of a home water filter (the tap water cost is so low that you can barely tell the difference in the slope of the line). In one case I gave the bottled waters a $200 head start, as if you choose to install a $200 home water filtration system. In the second bottled water gets a $300 head start, for a slightly more expensive filter. 

Let's take a look at the results, in graph form (click to enlarge).
The horizontal axis is time in days, with the entire length being 365 days.
The vertical axis is cost, with the entire height being $1500, as you can see some of the prices easily eclipsed this mark, I will include the year-long cost for each at the end.

As you can see the only difference in the two graphs is the height of the tap water plus water filter line on the graph. The point of intersection between the lines is when the costs are equal, after that point it's money saved. What is the conclusion then? It's apparent from the graphs that it's cheaper to choose tap water, even if you purchase an expensive water filter. Here are the final numbers (colors correspond with the graphs):

If you drink tap water without a filter for a year it would cost $0.59 (yes, that's 80 ounces a day for the entire year). With the filters the one-year cost is $200.59 and $300.59.

If you buy expensive, $1.79 bottled water for a year it would cost $3,092.78.
The $200 filter and tap pays off in 24 days, the $300 filter pays off in 36 days.

If you buy moderately priced, $1.00 bottled water for a year it would cost $1,727.81
The $200 filter and tap pays off in 43 days, the $300 filter pays off in 64 days.

If you buy cheap, $0.69 bottled water for a year it would cost $1,192.18.
The $200 filter and tap pays off in 62 days, the $300 filter pays off in 92 days.

If you buy 24 packs of bottled water for a year it would cost $359.24.
The $200 filter and tap pays off in 204 days, the $300 filter pays off in 306 days.

If you buy 5 gallon water coolers for a year it would cost $413.16.
The $200 filter and tap pays off in 176 days, the $300 filter pays off in 265 days.

Conclusion: go with tap water. Even if you need to buy a filter to maintain your health or taste preferences it will pay off well within the year.