Yes. Lets take your deal. It is worth 180K but you are getting for 120K. You are putting 3% down for owner occupy. Another option pay $123,600 and have the seller pay for 3% of your closing cost. You can get in with zero out of pocket or close to. Bank won't care and this is done a lot. You might be able to go as high as $128,600 and ask for seller to give 5K in repair allowance for counter, carpet, paint. You walk away from escrow with a check. This was done a lot in the day not sure if banks will allow but seems doable if justifiable. I am escrow now with 9K allowance for new windows. Will see in 3 weeks when we close.
Back to you, even if you don't do above 120K 3% down. With fees and closing costs your loan will still probably be 120K when you are done. Home closes and you have a new loan for 97 % financing on a 30 year fixed.
In one year your purchase becomes seasoned. If you refi or get a new loan they will no longer go off purchase price they will go off a new appraisal. If you just want to get the pmi off you can get an appraisal and if it appraises for anything over $153,846 that makes 120K 78%. It should be 80% but in Wells literature they say they automatically drop off at 78%. You do have to use a Wells Fargo Appraiser. Get this information and cost up front. Not sure your area but in our area appraisals for SFR run $300-500. No need to refinance.
At the year mark you can get a HELOC which is just a line of credit. Depending on credit and home and rate will determine how much you can take out. Pretty easily 80% possibly 90% as much as 100%. I think Wells only does 80%. Your house appraises for $180K @ 80% that's 144K minus your first of $120 leaves $24K in a line of credit. It doesn't sound like a lot but it is powerful. A HELOC isn't like a first mortgage. It usually is free or up to a couple hundred dollars to apply. They will do a new appraisal. If you go with Wells I would check if your house appraises for the 180K if they will drop the PMI. Kill 2 birds with one stone. Sometimes they will not require a full appraisal just a drive by. Once you have the line of credit (goes through relatively quickly) you are good to go. You can use the money for whatever you want go on a trip, buy a car. Don't do either of these. What you do is find an investment property and use it for your down payment.
Wells isn't the only place. If you start looking around at billboards for your local banks or credit unions you will start to see advertisement for equity lines. They start coming out in the spring when there is a huge push for home improvement. You can do a quick google search for 100% LTV HELOC. The higher LTV the higher rate you will pay. Keep in mind this is an equity line not a loan. Many times the first 10 years is just interest only payments. This is great for keeping your payment low. After 10 years your outstanding balance converts to a payback faze usually 10-15 years and payment will jump drastically many times doubling so plan accordingly. Like I said this a line. You can pay down as little or as much as you like. When it is paid down it will free it up again. When the market started to crash and prices dropped the banks either froze or lowered equity lines not giving you access to your equity. Use wisely. If you transfer equity to another property that cash flows you should be fine. Find something that will appreciate. This equity line would have come in handy for that town home purchase you had to pass on. They are a great resource and tool for building your real estate portfolio. From down payments to repairs to vacancy. They are nice to have.