Author Topic: How would you convert PMI to an APR?  (Read 3030 times)

Frugalicious

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How would you convert PMI to an APR?
« on: October 09, 2014, 04:48:52 PM »
How would you go about converting the dollar amount of PMI into an APR?  Let's say you have a house and the balance on the mortgage is \$200k.  The PMI on the house is \$95 a month.  What is the math to convert?

Is it as simple as (95X12)/200,000?  Or am I missing something?

Thanks.  For some reason this feels like it shouldn't be that hard, but I'm doubting my approach.

Hotstreak

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Re: How would you convert PMI to an APR?
« Reply #1 on: October 09, 2014, 04:57:22 PM »
That would be accurate for your first payment.  Since PMI doesn't decrease as your loan balance decreases, you will find a higher % after each payment.

I'm curious what the practical application of this would be.  Do you have the choice between a higher APR loan, and one with PMI?

Frugalicious

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• Location: Atlanta, Georgia
Re: How would you convert PMI to an APR?
« Reply #2 on: October 09, 2014, 05:24:28 PM »
The application is to figure out which mortgage is costing the borrower more money.

Assuming, loan 1's balance is \$80k, with an interest rate of 6.75% (yikes!), but no PMI.

Loan 2's balance is 200k, with an interest rate of 4.375%, PMI of \$95 per month.

The borrower was attempting to pay down loan 2 to get rid of PMI, but the effective rate is lower on loan 2, even with PMI.

That's what I was trying to get at.

Hotstreak

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Re: How would you convert PMI to an APR?
« Reply #3 on: October 09, 2014, 05:27:08 PM »
Okay, that makes sense.  Can you take the calculated APR's, including PMI, for each month until 80% LTV and average those?  That would be a great comparison to the other fixed rate loan with no PMI.

Frugalicious

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• Location: Atlanta, Georgia
Re: How would you convert PMI to an APR?
« Reply #4 on: October 09, 2014, 05:34:55 PM »
The only issue is that the PMI amount seems to reset yearly.  But, there's enough of a difference in rates between the two to make a convincing case for focusing on loan 1 (if excess cash MUST be sent to a mortgage, that is).

retired?

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Re: How would you convert PMI to an APR?
« Reply #5 on: October 09, 2014, 06:44:15 PM »
This is similar to the Q how much does an HOA fee cost?  What is the buying power that it costs.

My answer, in Excel format, would be:

mortgage rate is r
PMI is i
Principle is P
Number of months is N

The mortgage payment for the loan only is pmt(r/12,N*12,-P) = K

You are actually paying K + i

So, to determine the effective rate, you want to solve for R such that

K + i = pmt(R/12,N*12, -P)

It's a useful exercise b/c it answers the question "by not putting down 20% to avoid PMI, I am effectively paying R rather than r".

The twist that makes it a little harder is that PMI will disappear as soon as you reach 20%+ equity (not automatically, you need to contact the bank and then cancel).  If you are interested, I can provide some formula for that.  No PMI would be reached within 5-7 years.  In this case you have:

Principle = sum over time with PMI (discount K+i at rate R) + sum over time after PMI is not required(discount K at rate r)