You can generally expect to spend about 10% of the cost of the house in fees and taxes to sell it, maybe 3% to buy it, and interest is front loaded.
If you’re gonna be in a $100k house for 3 years, that’s $3k up front, probably $6k/year in mortgage interest, $4k/year in property taxes, and $10k to sell it when all is said and done. So let’s add that up – it’s about $45k, which is $1200/month. If you could rent that house for $1200/no and put any leftover money into a savings account, you come out ahead of someone who bought it and sold it. That’s your best case if you don’t need to do any repairs on it
Home ownership “builds equity” when you’re holding a house long enough that
1. It goes up in value significantly due to appreciation / inflation
2. You got in at a low interest rate
3. You kept it long enough to be in the middle-later part of the mortgage when proportionally less goes to interest and more goes to principle
4. You kept it long enough that the various buying/selling fees (“closing costs”) are more spread out
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