FWIW – In my experience, the cost of a mortgage payment plus private school tuition is rarely less than the cost of a mortgage payment in a place where you like the school. On average, private elementary schools in SD are about 10,000/yr. (The big names are much more than that and high school is closer to $20,000/yr, even at an average school). With any extras for uniforms, etc. you are probably looking closer to $1000/month. If there are two kids, there’s no question you’re better off buying in a good school district (plus you get the interest deduction and appreciation).
