Pay off student loans or eliminate mortgage insurance?

[samuelri]

Greetings.  I am trying to decide whether it makes sense to pay off a couple of student loans or put that money towards home equity to eliminate mortage insurance.  Here are the details:

1.  PMI = $208 per month and 79 payments remaining until 80% LTV.  To eliminate PMI now would require a lump sum of $37,412.

2.  Student loan #1 @ 6.50% rate = $198 per month and 174 payments remaining.  Student loan #2 @ 8.40% rate = $153 per month and 111 payments remaining.  To elimate both payments now would require a lump sum of $33,600.

Which makes more sense?  I appreciate the financial wizardy and insight.

[Numbers Man]

I would pay off the student loans due to the high interest rates.

[samuelri]

That's what I thought, too, but then did some math.  If I pay off student loans now, I save $17,900 in interest.  If I get rid of PMI, I save $16,432 in PMI payments, but I also have that equity in my home.  The $33,600 I pay to eliminate the student loans is just gone.

However, the reduction in monthly payment for getting rid of the student loans is much greater and that's why I'm stuck.

[Mississippi Mudstache]

Could you give us some more information?

Original purchase price of home:
Mortgage balance:
Mortgage interest rate:

[samuelri]

Sure and thanks for the help.  The original purchase price was $279,900 and the mortgage balance is $261,332 with a rate of 3.625%.

[Mississippi Mudstache]

The effective interest rate of your PMI payment is 6.67%. However, you will not only be getting rid of the PMI payment, you will also be reducing the principal on your home, so you have to consider the $37,000 that isn't compounding annually at 3.625%. That brings the total effective interest rate savings to 10.3% if you pay down the mortgage to 80% first. So that's what I would do.

[Mississippi Mudstache]

How are you getting 6.67%? I'm doing (208*12)/261,332 = .955% which would save 4.58% on the amount paid off (plus any adjustment for taxes if itemizing)

You're using the wrong denominator. The PMI payment goes away entirely once the OP has paid $37,412 towards principal, so divide by that instead of $261,332.

[Mississippi Mudstache]

Yes, it's more complicated than my simplistic calculations would suggest. The reason is that the $208/mo PMI payment is not really a debt payment, since its monthly payment does not contain any principal reduction. The numbers that I ran are based upon savings given a lump sum payment. Paying the loans down over a given period of time would yield a different result.

However, we don't know how much the OP can pay monthly, so we can't calculate anything else with the information given. I think paying down the high interest rate student loan would be a rational first step. The balance on that one should be in the neighborhood of $11,700, correct?

[Mississippi Mudstache]

Don't feel too bad - when I bought my current home I made the asinine mistake of taking out a USDA loan that bundled up all of the PMI payments and simply added them to my principal. My mortgage broker sold me on the loan because it reduced my monthly payments early on in the amortization schedule, but the downside that she left out (and I didn't take the time to research) is that I can never make the PMI payments go away! They are a part of my principal, so even if I sell the house today, I still have to pay several more year's worth of PMI payments. It was an incredible ripoff, and I'm glad that I've educated myself financially since then. At least my mortgage broker got some more money out of the deal, since it added about $10,000 to the loan amount.