but most mortgages don't have any penalty associated with refinancing, so paying a higher interest rate for 6 months ends up being a negligible amount. Most mortgages would allow you to refinance after 6 months. The only money you'd be out is for the extra appraisal.
Many people wrongly fight for the lowest rate when they would save a lot more money by getting out of PMI ASAP.
Say you buy a house for $200,000. You got a good deal, so the house is actually worth $220,000. You put 10% down, so you only owe $180,000 after the initial loan. You pay a higher rate for 6 months until you can refinance, but this is well worth it because the breakeven point on a no-cost vs. the lowest rate is usually about 7 years.
After 6 months you refinance. 50/50 chance that rates went down, so you end up paying even less per month. But the real benefit is that now you have 20% equity in the house ($40,000), so you no longer have to pay any PMI. If it takes a year to get to that 20% equity, so be it - accelerate your payments if you can. Then you refinance, order a new appraisal, etc. and pay about $200/month less on your mortgage.