Assuming an appraised value of $185k (although higher would be better), you'd refinance into a new loan of $148k. Depending on your credit score, you could expect the new mortgage to come in somewhere in the 3.5%-3.875% range if you went with a conventional 30 yr fixed mortgage. This would save you $325-$360 per month by lowering your rate, lowering your loan balance, and dropping the PMI.
The key in determining if this makes sense for you is finding out what terms you could get on this $20k loan to pay down the balance. It's not a mortgage, it's more of a personal loan. You wouldn't want to make the new loan any longer than 6-7 years since that is how long you would be paying the PMI for.
In my opinion, if you could borrow the money from a relative or friend in the 5% range then it would probably make sense. $20k for 7 years at 5% is $283/month so you would save $40-$80/month. However, if you were borrowing this money from a bank then they will most likely charge you 8-9% or higher. If that's the case then the savings could be entirely wiped out by the cost of that 2nd loan payment and you would just be robbing Peter to pay Paul.
So find out what you could expect to pay for that 2nd loan, then I can run a detailed analysis for you to see if it makes sense. You may also want to look into a 401k loan if you have the ability to do this. That way you'd be paying back yourself so it might make more sense.
It's a tough call really, make sure you take into consideration the cost of the new loan, also, remeber that FHA loans have changed to where you are now stuck with PMI for the life of the loan! You financed last year so you are fine! Why not put that money towards paying down your principle? The new second loan will come with costs and a higher interest rate.
Be sure to factor in all of the costs, you might be better off putting the extra into your existing loan.
Give me a call to get started on the process.
NMLS #: 222407
One Mortgage, Inc.
119 E Palatine Rd #200
Palatine, IL 60067
It will show everything, be a guide for comparing Loans, and give you the info you need to see if you will be saving any money.
There are too many variables to answer intelligently. (and I don't feeling like showing my unintelligence.)