If you paid on a mortgage for 10 years and then refinance another 30 year fixed, you're adding 10 more years to your payments, I don't see how that saves money. But whatever.
Then you lack an understanding of basic finance...All you are seeing is the micro...the monthly payments and how long they are going to last. Let the interest work FOR you. If you pay for 10 years then refi into a new 30 year fixed, you can do several things. Allow me to illustrate:
If you borrowed $100,000 fixed at 7% for 30 years:
PMT = $665.30
...and by 2019, your remaining principal balance is $85812.38...more or less
Let's say you refi that amount into a new 30 year fixed under two assumptions:
1. In the 10 years you've been paying your mortgage consistently you have increased you credit score
2. In the same 10 years you have gotten raises, promotions, investments, etc. that have increased your income stream
Now you refi that remaining amount into a new 30 year at a LOWER RATE even though you can afford more...here's where the magic happens
Let's say your bank offers you 5.5% on 85812.38, which you accept. The PMT will be $487.23...However, you know you can comfortably spend $900 a month due to your income level...
You are contributing an extra $412.77 to principal. In this manner your new 30 year fixed that originated in 2019, that would have lasted until 2049 is up in November of........
2029
That's 10 years earlier than the original mortgage that you got in 2009.
Interest paid on a full 30 year amortization at 7% = $139,508.90
Interest paid on a full 30 year amortization of the refi amount = $89,591.59
Interest paid by 2019 on 1st mortgage at time of refi = $65,648.68
Interest paid on abbreviated amortization schedule after making extra principal payments = $27,255.02
Now, assuming that you WERE going to refi in 2019, the plan saved you:
89591.59 - 27255.02 = $62,336.57
That's what I call making home affordable