**Should I pay extra till I get rid of PMI?**

I would say usually that answer is yes. I hear most PMI's add an equivalent .5% to your payment, but since they are removed after 20% equity, the payoff is usually worth it especially the closer you are to 20%. But if you just want a quick formula. For PMI add .5% to the interest in any above formula.

Apologies for revising a somewhat old thread, but there seems to be a large misconception of the financial hit that is PMI. The most common approach I see for modelling the cost of PMI is the one given by FIPurpose, which is to simply add the PMI percentage to the mortgage percentage, in which case the expected return of mortgage plus PMI would be significantly less than the historical returns from stock (and hence a sound financial decision). Unfortunately, this is a severe under-representation of the true cost. The correct formula to represent PMI cost is

Effective Interest Rate (PMI) = Interest Rate (Mortgage) + Interest Rate (PMI) * (Mortgage-to-Loan-%) / (Mortgage-to-Loan-% - 80%)

So to use an example, if someone has the option for a 4% mortgage and is debating whether to put down 20% versus 10% with 0.5% PMI, the effective interest rate for the extra 10% will be

4%+0.5%(90%/(90%-80%))=8.5%

Since this result is below the generally agreed upon historical expected return for stocks (let's say 7%), PMI in this case is not good debt (unlike the rest of the mortgage). In fact, in almost all cases, PMI is a bad bet (not that some people haven't gotten ahead with PMI and some luck).

Edit to add:

For those less mathematically inclined, let's use a specific example. Say we are in a high cost-of-living area and are purchasing a $1M house (with a 4% interest rate offer). We are offered 0.5% PMI up to 90% loan-to-value. In this case, if we take the PMI, for the option of borrowing an extra $100k we get to pay $8500 per year (8.5%). This can be broken up to the mortgage rate cost on the extra $100k ($100k*4%=$4k) plus the cost of PMI on the full loan value ($900k*0.5%=$4.5k).

What makes PMI even worse than the numbers indicated is that as the loan gets paid off, the PMI doesn't decrease. So for the same example, say you took the PMI route and are now down to the last $1000 to get under an 80% loan-to-value amount. At this point you are effectively paying $4540 per year (PMI plus mortgage rate on the remaining $1000) to borrow $1000, resulting in an effective interest rate of 454%! But wait, it gets worse. The bank isn't required to automatically shut off PMI until you hit 78% loan-to-value, at which point you've passed an infinite interest rate on borrowed money and are now simply paying the bank an ignorance fee.

To determine whether PMI is a good bet, you really need to take the expected returns from stock versus the expected savings and returns from the lower mortgage payment and no PMI over the duration of the 30 year mortgage. In most cases, no PMI wins handily, and this is before taking risk into account.