PMI Question

[StashthatCash]

Wanted to get your guys' opinion on my PMI situation.  My wife and I put down 15% (I know face punch deserved) and got a 30 year loan with a 3.375% rate.  Our current PMI charge is $43.20 per month.  My question is does it make sense to put more money towards investments with the hopes that the market keeps doing well?  Or do we pay down that loan to get rid of the PMI all together (have the cash needed to do so).
Thank you

[inline five]

It costs around $500/yr to pay PMI

How much will you have to pay off to get below 78%?

More info needed.

[StashthatCash]

Sorry didn't know how much info to put in. 
Would need to pay $10,200 give or take a few bucks to get rid of PMI.

[VoteCthulu]

You need to look at your loan to find out how PMI can be removed. Sometimes it can't be removed for X years, sometimes you need a new appraisal showing the remaining value is less than 80%, and others just want the principle to be over 20% of the original loan value.

[Bicycle_B]

VoteCthulhu raised important points, but I'll assume that you covered them en route to getting your estimate of $10,200 invested to get back 43.20 x 12 = $518.40/year. 

Don't hope about the market, just assume it will give ordinary returns, and analyze the decision based on that.  Using 5% plus inflation as a typical market return, I'd say pay down the loan.  Example analysis follows, but do your own math to decide.

Expected investment return = 5% projected market return + 2% inflation = 7%.

Expected return on loan payoff = 3.375% + (518.40/10,200) = 3.375 + 5.08% = 8.455%. 

The return on the loan payoff appears higher.  Plus, it's guaranteed, while the market return isn't.

[Cwadda]

(I know face punch deserved)

No, it's not.  The idea that people should only put 20% down is archaic and cliche.

Bicycle_B put out the math well.  +1 for his/her advice.

[boarder42]

The math is incorrect and makes it look like a larger return than it is. It has to be taken against the entire value bc once the olmoney is in the house it no longer compounds at market rates.

I'm on my phone and don't want to lay out the math right now.  But in short OP it's not beneficial over a 30 year mortgage to do this. Maybe MDM or another will show up and do the math for you correctly. Or I'll lay it down later.

In short you don't add them together you take it as a percentage of the total loan then add it together

[druth]

The math is incorrect and makes it look like a larger return than it is. It has to be taken against the entire value bc once the olmoney is in the house it no longer compounds at market rates.

Isn't it still compounding though?  That's money that I no longer have to pay 5% on.  Could somebody explain this better?

Little bit of a hijack, but nearly the same question as OP.  I'm in a similar position, and my question is does this extend even as far as tax deferred savings?

In my case I need to pay 20k to no longer pay 110$/month in PMI, so 6.6% in one year, plus my mortgage at 4% is 10.6% total(!).  At that point should I make withdrawls from my Roth in order to pay it.  Obviously, only principle that wouldn't get a penalty.

[boarder42]

This question comes up alot we really should sticky the formula you should use to calculate this properly.

[boarder42]

So this is incorrect

Expected return on loan payoff = 3.375% + (518.40/10,200) = 3.375 + 5.08% = 8.455%. 

the 518.40/10200 must be taken as a percentage of the total loan b/c that is how it fundamentally works the 518 should be included in the total monthly payment to determine the real rate.

so to really give you your effective rate we need to know what your loan payment is P and I separate and the total mortgage balance remaining. 

[Bicycle_B]

So this is incorrect

Expected return on loan payoff = 3.375% + (518.40/10,200) = 3.375 + 5.08% = 8.455%. 

the 518.40/10200 must be taken as a percentage of the total loan b/c that is how it fundamentally works the 518 should be included in the total monthly payment to determine the real rate.

so to really give you your effective rate we need to know what your loan payment is P and I separate and the total mortgage balance remaining. 

Not understanding yet.  Why is the 518.40 related to the total loan at all?

Continue correcting me if I'm wrong, but OP gave 43.20 per month as the PMI charge.  $43.20 x 12 = 518.40, so that's the annual amount of PMI to be saved, is it not?  Since the OP said $10,200 of the loan needs to be paid in order to produce this savings, the savings due to the PMI payment can be calculated as a percentage of $10,200 - right?

Of course, if OP pays down $10,200 of the loan, OP also saves the 3.375% interest rate x 10,200.  Why isn't the total savings the loan interest saved plus the PMI saved? 

On reflection, I get that the calculation I gave is sort of crude, because it implies that the 8.4% combined rate lasts for the length of the loan, when it doesn't.  The PMI would disappear at some point and the return would be only 3.375% after that point.  It would be more accurate to calculate the savings per month times the number of months and get a total gain amount, then compare it to the gain during the same period from investing the $10,200 in financial investments.  But neither method involves the total loan, so... I await further comment.

PS.  This came up before and I never understood the other side.  Honestly curious!

[boarder42]

So let's say it's a 200 k loan. You would pay 6600 give or take in interest during the early years   plus the 518.4. Against the 200k. So 6600 plus 518.40 divide that by the 200k and you have an effective date of 3.55%.  You could also add this up monthly. Bc it changes monthly.  Simply add the PMI to the interest you're paying each month multiply by 12 and divide by what you owe. It will increase since the PMI doesn't go down over time.

Does that make sense.

[Bicycle_B]

So let's say it's a 200 k loan. You would pay 6600 give or take in interest during the early years   plus the 518.4. Against the 200k. So 6600 plus 518.40 divide that by the 200k and you have an effective date of 3.55%.  You could also add this up monthly. Bc it changes monthly.  Simply add the PMI to the interest you're paying each month multiply by 12 and divide by what you owe. It will increase since the PMI doesn't go down over time.

Does that make sense.

I can follow the calculation mathematically, but don't see how it could be useful.  How does it apply to decision making?

As I understand the original post, the original poster is trying to decide whether pay down the loan to point of not paying PMI, or to invest that same amount of money into financial investments.  Calculating the amount of savings produced by the mortgage paydown and the foregone PMI is relevant to that decision, as is the amount of expected gain from the financial investments.  He/she needs to compare the amount of gain in the two alternatives in order to decide which option is more profitable.  How is the percentage of the overall loan relevant to the OP's question?

[boarder42]

you miscalculated the return on investment by looking at it in a vacuum.  the ROI of paying it down faster is around 3.5% right now.  much worse than the investment alternative.

that 3.5% is based on a 200k mortgage in the early stages- we'd need real numbers from the OP to actually calculate it.  and that 3.5% will in fact rise as OP is closer to payoff date but not enough to pay it down faster.

another way to look at it would be to take the 518 dollars a year and invest it annually vs a lump sum investment of the payoff of 518 for as many years as PMI would remain on the loan in normal paydown circumstances. 

but again we dont have nearly enough information still from OP to tell them they are better paying it down vs investing.

if we assume it takes a long 10 years to pay off the last 5% then the numbers compounding at 7% would be

518.40 per year for 10 years - 7663

10200 compounding for 10 years - 20064

the 518.40 doesnt even catch up to the initial investment of the 10200 in 10 years

so investing wins.

[Joel]

VoteCthulhu raised important points, but I'll assume that you covered them en route to getting your estimate of $10,200 invested to get back 43.20 x 12 = $518.40/year. 

Don't hope about the market, just assume it will give ordinary returns, and analyze the decision based on that.  Using 5% plus inflation as a typical market return, I'd say pay down the loan.  Example analysis follows, but do your own math to decide.

Expected investment return = 5% projected market return + 2% inflation = 7%.

Expected return on loan payoff = 3.375% + (518.40/10,200) = 3.375 + 5.08% = 8.455%. 

The return on the loan payoff appears higher.  Plus, it's guaranteed, while the market return isn't.

This is how I would look at this. Pay off enough to get rid of PMI!

[boarder42]

VoteCthulhu raised important points, but I'll assume that you covered them en route to getting your estimate of $10,200 invested to get back 43.20 x 12 = $518.40/year. 

Don't hope about the market, just assume it will give ordinary returns, and analyze the decision based on that.  Using 5% plus inflation as a typical market return, I'd say pay down the loan.  Example analysis follows, but do your own math to decide.

Expected investment return = 5% projected market return + 2% inflation = 7%.

Expected return on loan payoff = 3.375% + (518.40/10,200) = 3.375 + 5.08% = 8.455%. 

The return on the loan payoff appears higher.  Plus, it's guaranteed, while the market return isn't.

This is how I would look at this. Pay off enough to get rid of PMI!

then you're looking at it entirely wrong see my post above yours. 

[Joel]

You are assuming guaranteed returns of 7% on that money if invested. That’s quite optimistic. You also are not factoring in the reduced interest that will be paid on the mortgage as a result. I do not think the answer is nearly as black and white as your post makes it out to be.

[sherr]

You are assuming guaranteed returns of 7% on that money if invested. That’s quite optimistic. You also are not factoring in the reduced interest that will be paid on the mortgage as a result. I do not think the answer is nearly as black and white as your post makes it out to be.

It is that black-and-white. The calculated 3.5% Return On Investment is the "reduced interest that will be paid on the mortgage" plus the tiny fraction of a percent that is the PMI going away. Market returns are of course not guaranteed, but 5% + inflation is actually pretty conservative. Long-term historical average is more like 7% + inflation. 7% is as good a place as any to start answering an "Invest or pay off PMI" question.

[MilesTeg]

If you do pay down a large chunk to get rid of PMI, then inquire with your lender about doing a mortgage recast with the payment. A recast is where the lender re-sets your loan term and recalculates your payment without changing your rate or any other part of the loan. Typically a lender will require a 10% lump sum of the remaining balance plus a moderate fee ($100-200). It's like a very cheap refinance. If you have a good rate (around 4%) it's something to consider (if you do a lump payment anyway) as it will reduce your monthly payment obligation. HOWEVER, it will cost you more in interest UNLESS you pay more than the new minimum (how much more to break even is down to some math).

[Joel]

You are assuming guaranteed returns of 7% on that money if invested. That’s quite optimistic. You also are not factoring in the reduced interest that will be paid on the mortgage as a result. I do not think the answer is nearly as black and white as your post makes it out to be.

It is that black-and-white. The calculated 3.5% Return On Investment is the "reduced interest that will be paid on the mortgage" plus the tiny fraction of a percent that is the PMI going away. Market returns are of course not guaranteed, but 5% + inflation is actually pretty conservative. Long-term historical average is more like 7% + inflation. 7% is as good a place as any to start answering an "Invest or pay off PMI" question.

By doing it that way, you guys are entirely ignoring the fact he will be avoiding 3.375% interest on the mortgage since he paid down the money.

$10,200 paydown needed to remove PMI
3.375% interest rate
$344.25 annual interest saved ($10,200 * 3.375%)
$518.40 annual PMI avoided ($43.20 * 12)
$862.65 annual savings ($344.25 + $518.40)
8.46% annual return ($865.65 / $10,200)

If you think you can get better guaranteed returns than 8.46%, you should put your money there. Otherwise, paying down the mortgage just enough to get rid of PMI is the better investment. That is black and white.

[sherr]

You are assuming guaranteed returns of 7% on that money if invested. That’s quite optimistic. You also are not factoring in the reduced interest that will be paid on the mortgage as a result. I do not think the answer is nearly as black and white as your post makes it out to be.

It is that black-and-white. The calculated 3.5% Return On Investment is the "reduced interest that will be paid on the mortgage" plus the tiny fraction of a percent that is the PMI going away. Market returns are of course not guaranteed, but 5% + inflation is actually pretty conservative. Long-term historical average is more like 7% + inflation. 7% is as good a place as any to start answering an "Invest or pay off PMI" question.

By doing it that way, you guys are entirely ignoring the fact he will be avoiding 3.375% interest on the mortgage since he paid down the money.

$10,200 paydown needed to remove PMI
3.375% interest rate
$344.25 annual interest saved ($10,200 * 3.375%)
$518.40 annual PMI avoided ($43.20 * 12)
$862.65 annual savings ($344.25 + $518.40)
8.46% annual return ($865.65 / $10,200)

If you think you can get better guaranteed returns than 8.46%, you should put your money there. Otherwise, paying down the mortgage just enough to get rid of PMI is the better investment. That is black and white.

That's the whole point though, it's incorrect to look at it as a 1-year ROI because it's a 30-year mortgage.

It has to be taken against the entire value bc once the money is in the house it no longer compounds at market rates.

So your options are:
1) invest, get an average of 7% every year for 30 years
2) paydown mortage, get a guaranteed 3.375% every year for 30 years + some additional hard-to-calculate extra bit that represents the PMI fees going away.

The PMI fees are going to go away by themselves eventually without paying down the mortgage, so it's obviously incorrect to take the first-year fee reduction and assume that it will continue every year for the lifetime of the loan. It's exactly the same and equally incorrect (but less obviously) to only look at the first-year ROI and make decisions based on that number.

Let's say for the sake of argument that the PMI would have gone away naturally at the end of year 2. So then the value of paying down the mortgage is 8.46% for year 1, 8.46% for year 2, and then 3.375% for the remaining 28 years. That's obviously going to be way less than 7% for 30 years. (It's a 298% vs 761% 30-year ROI, in case you were wondering).

[boarder42]

You are assuming guaranteed returns of 7% on that money if invested. That’s quite optimistic. You also are not factoring in the reduced interest that will be paid on the mortgage as a result. I do not think the answer is nearly as black and white as your post makes it out to be.

It is that black-and-white. The calculated 3.5% Return On Investment is the "reduced interest that will be paid on the mortgage" plus the tiny fraction of a percent that is the PMI going away. Market returns are of course not guaranteed, but 5% + inflation is actually pretty conservative. Long-term historical average is more like 7% + inflation. 7% is as good a place as any to start answering an "Invest or pay off PMI" question.

By doing it that way, you guys are entirely ignoring the fact he will be avoiding 3.375% interest on the mortgage since he paid down the money.

$10,200 paydown needed to remove PMI
3.375% interest rate
$344.25 annual interest saved ($10,200 * 3.375%)
$518.40 annual PMI avoided ($43.20 * 12)
$862.65 annual savings ($344.25 + $518.40)
8.46% annual return ($865.65 / $10,200)

If you think you can get better guaranteed returns than 8.46%, you should put your money there. Otherwise, paying down the mortgage just enough to get rid of PMI is the better investment. That is black and white.

this math is wrong if you cant see that i dont really know how to help you understand it better.  the 43.20 per month needs to be looked at as additional interest on a per payment basis.  not compared to the small 10200 dollars it would take to get rid of the 43.20 per month. 

you're skewing the results and doing incorrect math to make it look beneficial... its not... see my post above.

the minor interest per month saved could be added to the 518.40 per month and you could run this out for 30 years and then invest the last 3 months of dollars it will never catch up under normal market conditions.  which we all assume to be true b/c thats how we plan to FIRE.

Debt and PMI aversion are two of the worst things talked about here.  My buddy bought a house with 3.5% down and in one year when he owned 5% of that house he REFI'd to a rate at 3.5% with no PMI - his rate went up 1/8th of a point due to the lender buying out his PMI when he refi'd ... you try getting 3.5% today with perfect credit on a 30 year.... you cant do it. 

I always say if the house is the right deal and it makes sense over renting its never to early to buy... you can always refinance if rates go down .. OP you'll likely never get 3.375% again on a 30 year so make the most of it and dont pay down your PMI early.  Invest that money. 

I have a follow up question - OP are you maxing your tax advantaged accounts already b/c if not then its a monumental landslide in favor of putting that money into an index fund.

[sherr]

So your options are:
1) invest, get an average of 7% every year for 30 years
2) paydown mortage, get a guaranteed 3.375% every year for 30 years + some additional hard-to-calculate extra bit that represents the PMI fees going away.

The PMI fees are going to go away by themselves eventually without paying down the mortgage, so it's obviously incorrect to take the first-year fee reduction and assume that it will continue every year for the lifetime of the loan. It's exactly the same and equally incorrect (but less obviously) to only look at the first-year ROI and make decisions based on that number.

Let's say for the sake of argument that the PMI would have gone away naturally at the end of year 2. So then the value of paying down the mortgage is 8.46% for year 1, 8.46% for year 2, and then 3.375% for the remaining 28 years. That's obviously going to be way less than 7% for 30 years. (It's a 298% vs 761% 30-year ROI, in case you were wondering).

I decided to just calculate it. The crossover happens in year 22, so if your PMI would go away naturally sometime in the first 21 years (it will) then you can expect to make more money in the stock market.

x = number of years the PMI would have stuck around normally
Value of investment: 1.07^30
Value of mortgage prepayment: 1.0846^x * 1.03375^(30-x)

And that's not even beginning to consider other factors, like that the principal of your mortgage does not adjust with inflation (so in 20 years your salary will theoretically have adjusted with inflation so you're paying your 2017-dollar mortgage with 2037-inflated-dollars). If inflation goes above your 3.375% rate (which it most certainly has in the past!) then pre-paying your mortgage would have a negative real value.

No one likes the idea of debt, but in today's world of absurdly-low interest rates it's practically never a financially sound decision to prepay your mortgage.

[boarder42]

found my old posts ... here is one way to calc it correctly

https://forum.mrmoneymustache.com/ask-a-mustachian/getting-rid-of-pmi-what-'return'-would-i-get-for-paying-down-my-mortgage/msg1561643/#msg1561643

Here is another way that gets you to the same end result. 

https://forum.mrmoneymustache.com/ask-a-mustachian/getting-rid-of-pmi-what-'return'-would-i-get-for-paying-down-my-mortgage/msg1561921/#msg1561921

I didnt run thru Sherr's formulat but you're PMI is ridiculously low OP you should not be paying it down.

[Bicycle_B]

Well, I'm ready to pivot!

Sherr's formula makes sense to me.  The basic explanation that once you make additional payments on the mortgage, they stay invested also makes sense to me, at least until the house is sold or the note is refinanced.

I went year by year in a spreadsheet.  It quickly became clear that, based on the numbers we are using (3.35% interest on underlying mortgage, 7% expected return on financial investments, 2 years before PMI would be paid off anyway) the financial investments win out quickly after the normal time to pay off the PMI.  The PMI payoff was ahead for the first two years, but by the end of year three, the financial investments were already winning.
 
The process takes a lot longer if investment returns are lower.  At 5% returns, it took four years for the financial investments to pull ahead.  Obviously the real result will depend on actual investment returns.  If they're negative for a while due to market downtown, it could take a much longer time to catch up!  But based on historical norms, it seems likely that OP would be better off in financial investments if he/she expects to hold the house at least four more years.

[StashthatCash]

Wow thanks for all the responses since the last time I was on.  I think based on the arguments below I would agree that I am better off investing vs paying down the principal of the loan to get rid of the low PMI costs.  Thanks again everyone!