The fastest way to eliminate PMI?

[Justin Jolliffe]

I'll cut straight to the point:

I am purchasing a 3 family to house hack and I want to get rid of PMI as soon as possible. Here are the numbers.

Purchase Price: $335,000

Gross Income $3600.

I have the money to put down 3.5%, even 5%, but which one is better to do? As of right now, I am thinking that placing 3.5% down on the house and putting my leftover money in the stock market, and consistently adding to it every month for a few years until I have a reasonable chunk of change. Then, I can dump it all into the house (Assuming the stock market does well) to reach a 20% equity stake, refinance and eliminate PMI.

I just can't stand the thought of my money sitting there in the house if it isn't working for me.  Until I get to the 20% mark, it seems foolish to put it towards the principal other than to marginally lower interest payments.  I am betting the stock market will do at least better than that option.

Am I approaching this the right way?