The Money Mustache Community
Learning, Sharing, and Teaching => Ask a Mustachian => Topic started by: Frugalicious on October 09, 2014, 04:48:52 PM
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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.
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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?
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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.
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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.
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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).
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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)