Regardless of which route you choose, before adding extra money to your existing mortgage with the express intent of ridding yourself of PMI, you should contact the lender. In many mortgages, PMI does not automatically go away by hitting a specific amount of equity. Often, you must also have had the loan for a specific amount of time, typically 5 years. This may not be the case with your loan, but it is worth checking with a quick phone call. The last thing you want is to have the worst of both worlds where you put $14k in and still get the pleasure of paying PMI for another few years - so no investing and still PMI.
You may end up needing to refinance to completely get rid of PMI, in which case, you’ll also need to consider the added closing costs in your calculations.
Another consideration - where is the $14k coming from? In other words, are you about to drop any possible safety net into paying down the mortgage (or investing)? I ask because you only financed the house a couple of years ago. I assume if you had the money at the time, you would have put 20% down and never had PMI to begin with. If this is the case, I recommend caution putting the larges amounts of your savings into either PMI or an investment; set at least a little aside just in case.
On whether to invest or not, I think this is fairly straightforward. How much is PMI/yr + loan interest/yr - tax implications vs. reasonable returns - taxes on any investment (to my knowledge, there is no tax implication of PMI). $50/mo, or $600/yr is 4.285% of 14,000. You presumably save 3.75% on the $14,000, as well, though due to the mortgage interest deduction, the value of which depends on your marginal tax rate, the two combined could be anywhere from around 7% - 8%.
Can you do better than that investing when tax adjusted? I believe that it is possible, though the PMI + overall reduced interest is a sure thing.