Oh, yeah, I think that math is way off. Good, yes, but the savings are MUCH higher.
Firstly, I don't think you need gadgets. My kids, in sposies, wear huggies because they are the cheapest of the non-perfumed options. The others take my breath away and make my kids break out. And, with a newborn, we spend 20 to 30 every other week on diapers. At LEAST 12 changes a day. Every other hour around the clock, sometimes more. Every time you go through a box of diapers, you have spent the equivalent of one pocket diaper. So, when I use pockets, I figure not using sposies for one week buys me one cloth diaper. Obviously, if you buy one size (which did fit my kids from the beginning), and pockets, 20 is a lot of diapers. 20 weeks and you've bought a stash that will work until they are out of diapers.
And pockets ARE expensive.
10 Mommy's Touch one-size covers (highly recommend...very adjustable, great quality), and a stash of prefolds ($1 to $2 each) (or your old t-shirts to fold and snappi) and you're done.
10 covers (170.00)
24 small prefolds (24.00)
24 medium prefolds (36.00)
24 large prefolds (48.00) (which you probably won't need)
Total: 274.00 And that's ALOT of diapers. I have about 30 to diaper 2 kids, and that's plenty becuase they are yucky sitting around any longer than that anyway. And, you can use your prefolds for wiping noses, dusting shelves, and for changing pads. You don't need a sprayer, just flip off the solids.
You can easily get by on the cost of covers alone, by using t-shirts instead of prefolds.
And you can easily get by on 1/2 the prefolds, and covers, and not buy larges at all.
So, 5 OS covers, 12 small prefolds, and 12 medium prefolds cost less than $100. And will diaper your baby until they are potty-learned.
The fancier you get, and the more you buy, obviously, the more it will cost, but, yeah, cloth diapering is WAY cheaper.