Answers:

- Yes I'm adding interest costs... I'll rephrase my math with an example below.

- I do not plan on making extra payments, though, I'm tempted. Interest, like investments, compounds. Math is hard.

- If I refinanced, the purpose would have been to reduce the payment so I could invest more, in which case, I would no longer want to pay off my mortgage early. In that case, I would not make extra payments.

Sample Math:

Current mortgage, month one, the interest is $293.13 ($925 total payment, $631.87 goes to principal.) $0 left for investing (until mortgage is paid off.)

Refi mortgage month one, the interest is $348.75 ($525 total payment, $176.25 goes to principal.) $400 left for investing, earns $2.33.

I increased my interest payments by $55.62, but freed up $400, which I invested and earned an amazing $2.33. So the refi is worse by $53.29 even though almost half of my money is going towards a 7% investment which is clearly enough to pay for 3.875% in mortgage interest. (But since the interest rate increased for $105,000, it's a losing change in my finances.)

I adjusted my "formula" (Excel spreadsheet) to account for equity and I find that by the end of year 6, it actually starts to favor the investing / refi option, though.