Author Topic: Getting rid of PMI? What % "return" would I get for paying down my mortgage?  (Read 4785 times)

Bracken_Joy

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How do I do the math to find out if paying aggressively down past the point of PMI removal on my mortgage is worth it? I have no idea how to approach this =\

Numbers:
purchase price: $341k (we rolled $6k of closing costs in, not sure if the breakdown of the cost matters?)
original loan amount: $311k
remaining principal: $306.5k
base interest rate: 3.5%
PMI per month: $106.26
(For some reason the number 0.4% is sticking in my head for PMI rate? Dunno if that's helpful).

No prepayment penalties or minimum duration before PMI removal.

So first question, would 80% be 80% of $341k? It was appraised at $345k at the time, but reading online, it sounds like lenders use the lower of the two values, whether purchase price or appraisal.

Second question, what "return" would I get paying the mortgage down aggressively get me? So if I see the PMI as it's own loan, what rate would it be at? Thanks guys. This is beyond me.

Ebrat

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Here's how I would calculate it, assuming you're using 80% of 341k:

341000*.8=272800 <---this is what you need to be at to get rid of PMI

306500-272800=33700 <---this is the amount that you're paying PMI on

106.26*12=1275.12 <---this is the amount of PMI you're paying per year

1275.12/33700=.0378 <---this is the PMI expressed as a proportion of the amount you're paying PMI on

So you're effectively paying 3.5%+3.78%=7.28% to borrow that $33700.  Since the dollar amount of PMI stays the same as the loan balance shrinks, your effective interest rate goes up (e.g., if you were $16850 away from getting PMI, you'd be paying 3.5%+7.56%).

But, once you put that money into your mortgage, you can't really get it back out without refinancing or selling. So once you pass the point where you'd get rid of PMI via normal payments, your return on that money is only 3.5%. So it still might make sense to pay PMI, depending on how long you expect to be in the house, expected rate of returns on your investments, etc.

Bracken_Joy

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Here's how I would calculate it, assuming you're using 80% of 341k:

341000*.8=272800 <---this is what you need to be at to get rid of PMI

306500-272800=33700 <---this is the amount that you're paying PMI on

106.26*12=1275.12 <---this is the amount of PMI you're paying per year

1275.12/33700=.0378 <---this is the PMI expressed as a proportion of the amount you're paying PMI on

So you're effectively paying 3.5%+3.78%=7.28% to borrow that $33700.  Since the dollar amount of PMI stays the same as the loan balance shrinks, your effective interest rate goes up (e.g., if you were $16850 away from getting PMI, you'd be paying 3.5%+7.56%).

But, once you put that money into your mortgage, you can't really get it back out without refinancing or selling. So once you pass the point where you'd get rid of PMI via normal payments, your return on that money is only 3.5%. So it still might make sense to pay PMI, depending on how long you expect to be in the house, expected rate of returns on your investments, etc.

This is exactly what I was trying to figure out! Thank you! Hmm okay I guess I didn't think of it as a 'sliding' return but it makes sense, since it's a fixed amount monthly!

nick663

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It's implied by your first post but make sure the PMI does get removed when you pass the 80% threshold.  Some loans have PMI for the life of the loan and you'll have to refi to get out of it.

Also, some lenders require it to be paid down to 78% for removal.

dleavitt

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When did you purchase? If your market is anything like mine you may be over 78% LTV just through appreciation. I plan getting mine dropped through a new appraisal this fall when the two year waiting period on my refinance is up.

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clarkfan1979

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The closer you get to paying off the PMI the higher your rate of return. I'm $2000 or 12 payments away from paying off my PMI of $42/month or $504/year. If I send in a check for $2000 to my bank, I save $504 of interest over the next year, which is 20%.

Bracken_Joy

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It's implied by your first post but make sure the PMI does get removed when you pass the 80% threshold.  Some loans have PMI for the life of the loan and you'll have to refi to get out of it.

Also, some lenders require it to be paid down to 78% for removal.

I can request it at 80%, it automatically goes away at 78%. Thanks for checking that I knew that =) Always good to make sure!
When did you purchase? If your market is anything like mine you may be over 78% LTV just through appreciation. I plan getting mine dropped through a new appraisal this fall when the two year waiting period on my refinance is up.

Purchased in August. It may have appreciated that much already, stuff is selling high and fast right now =o

Here's the text on the website about "MI Information":
Quote
Under the Homeowners Protection Act of 1998, if your loan closed on or after July 29, 1999 as a single-family primary residence, you have the right to request that PMI be cancelled on or after either of these dates: (1) the date the principal balance of your loan is first scheduled to reach 80% of the original value of the property or (2) the date the principal balance actually reaches 80% of the original value of the property. PMI will only be cancelled on these dates if (1) you submit a written request for cancellation; (2) you have a good payment history; and (3) we receive, if requested and at your expense, evidence that the value of the property has not declined below its original value and certification that there are no subordinate liens on the property. A "good payment history" means no payments 60 or more days past due within two years and no payments 30 or more days past due within one year of the cancellation date. "Original value" means the lesser of the contract sales price of the property or the appraised value of the property at the time the loan was closed.

It sounds like only original value will be used? Not any new appraisals? Am I reading that right?
The closer you get to paying off the PMI the higher your rate of return. I'm $2000 or 12 payments away from paying off my PMI of $42/month or $504/year. If I send in a check for $2000 to my bank, I save $504 of interest over the next year, which is 20%.

So then would it make sense, as I get closer to reaching 80%, to increase paying it off then? Whereas it's less of a DO IT NOW right now, at functionally ~7.5%?

This is all theoretical right now- we don't have a big chunk of cash to move this instant. Just tweaking our money plan, as always =) 

dleavitt

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Call your mortgage servicer and ask?

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Bracken_Joy

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Call your mortgage servicer and ask?

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Well that would just be the obvious answer wouldn't it ;) But I like mustachians better!

Yeah, I'll probably call in a couple hours when someone might answer.

Heart of Tin

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Here's how I calculate the return of paying down your mortgage to get rid of PMI:

You need both the payment schedule for paying off PMI early and the payment schedule for not paying off PMI early. The schedule should extend to the end of your mortgage using the more time consuming method. That may be triggered by refinancing the mortgage, paying the whole mortgage off, or selling the house. Consider the difference between the two schedules as a series of cash flows. If there is a difference in equity between the two schedules at the end of the mortgage, consider this an additional cash flow. Find the internal rate of return for the series of cash flows.

For instance, if I consider you paying $400 extra per month towards your principle for the duration of PMI only, then you would have an internal rate of return of 3.557% over the 5 year term. Since neither schedule would be rid of PMI yet in that scenario, you would only really be benefiting from the rate of the mortgage. The same scenario over 7 years has a 5.659% internal rate of return. Here we see more of a benefit since PMI has been paid off in the abbreviated schedule, so extra cash is freed over the slower pay-off schedule. However, if we look at this scenario over 20 years, then the internal rate of return re-approaches the rate of the mortgage at 4.524%. Over the full 30 year term of the mortgage, the cumulative return would be 4.241%.

Your numbers will be different than mine above since I just assumed a scenario for the purpose of illustration, but they will follow the same approximate pattern.

boarder42

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Here's how I would calculate it, assuming you're using 80% of 341k:

341000*.8=272800 <---this is what you need to be at to get rid of PMI

306500-272800=33700 <---this is the amount that you're paying PMI on

106.26*12=1275.12 <---this is the amount of PMI you're paying per year

1275.12/33700=.0378 <---this is the PMI expressed as a proportion of the amount you're paying PMI on

So you're effectively paying 3.5%+3.78%=7.28% to borrow that $33700.  Since the dollar amount of PMI stays the same as the loan balance shrinks, your effective interest rate goes up (e.g., if you were $16850 away from getting PMI, you'd be paying 3.5%+7.56%).

But, once you put that money into your mortgage, you can't really get it back out without refinancing or selling. So once you pass the point where you'd get rid of PMI via normal payments, your return on that money is only 3.5%. So it still might make sense to pay PMI, depending on how long you expect to be in the house, expected rate of returns on your investments, etc.

this is close but not entirely correct you dont just add them together you have to add it as a value of the percent of the total loan making it look worse than what your numbers make it to pay down PMI.

Cwadda

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Here's how I would calculate it, assuming you're using 80% of 341k:

341000*.8=272800 <---this is what you need to be at to get rid of PMI

306500-272800=33700 <---this is the amount that you're paying PMI on

106.26*12=1275.12 <---this is the amount of PMI you're paying per year

1275.12/33700=.0378 <---this is the PMI expressed as a proportion of the amount you're paying PMI on

So you're effectively paying 3.5%+3.78%=7.28% to borrow that $33700.  Since the dollar amount of PMI stays the same as the loan balance shrinks, your effective interest rate goes up (e.g., if you were $16850 away from getting PMI, you'd be paying 3.5%+7.56%).

But, once you put that money into your mortgage, you can't really get it back out without refinancing or selling. So once you pass the point where you'd get rid of PMI via normal payments, your return on that money is only 3.5%. So it still might make sense to pay PMI, depending on how long you expect to be in the house, expected rate of returns on your investments, etc.

Hi, can you check my numbers for a similar situation?

Purchase price: $350,000
3.5% down, $12,250
Balance: $337,750
Interest rate: 4%
PMI: $240/month

350,000*0.8=280,000 <---this is what you need to be at to get rid of PMI

337,750-280,000=57,650 <---this is the amount that you're paying PMI on

240*12=2,880 <---this is the amount of PMI you're paying per year

2,880/57,650=.0499  <---this is the PMI expressed as a proportion of the amount you're paying PMI on

So I'm effectively paying 4.0%+5.00%= 9% to borrow that $57,650

Does this seem right?

boarder42, feel free to weigh in here

bigalsmith101

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Here's how I would calculate it, assuming you're using 80% of 341k:

341000*.8=272800 <---this is what you need to be at to get rid of PMI

306500-272800=33700 <---this is the amount that you're paying PMI on

106.26*12=1275.12 <---this is the amount of PMI you're paying per year

1275.12/33700=.0378 <---this is the PMI expressed as a proportion of the amount you're paying PMI on

So you're effectively paying 3.5%+3.78%=7.28% to borrow that $33700.  Since the dollar amount of PMI stays the same as the loan balance shrinks, your effective interest rate goes up (e.g., if you were $16850 away from getting PMI, you'd be paying 3.5%+7.56%).

But, once you put that money into your mortgage, you can't really get it back out without refinancing or selling. So once you pass the point where you'd get rid of PMI via normal payments, your return on that money is only 3.5%. So it still might make sense to pay PMI, depending on how long you expect to be in the house, expected rate of returns on your investments, etc.

Hi, can you check my numbers for a similar situation?

Purchase price: $350,000
3.5% down, $12,250
Balance: $337,750
Interest rate: 4%
PMI: $240/month

350,000*0.8=280,000 <---this is what you need to be at to get rid of PMI

337,750-280,000=57,650 <---this is the amount that you're paying PMI on

240*12=2,880 <---this is the amount of PMI you're paying per year

2,880/57,650=.0499  <---this is the PMI expressed as a proportion of the amount you're paying PMI on

So I'm effectively paying 4.0%+5.00%= 9% to borrow that $57,650

Does this seem right?

boarder42, feel free to weigh in here

Cwadda, you nailed it. PMI is biting you in the ass. You're paying 9% on that balance right now, and it only gets worse the closer you get to 80% loan/value.

boarder42

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Here's how I would calculate it, assuming you're using 80% of 341k:

341000*.8=272800 <---this is what you need to be at to get rid of PMI

306500-272800=33700 <---this is the amount that you're paying PMI on

106.26*12=1275.12 <---this is the amount of PMI you're paying per year

1275.12/33700=.0378 <---this is the PMI expressed as a proportion of the amount you're paying PMI on

So you're effectively paying 3.5%+3.78%=7.28% to borrow that $33700.  Since the dollar amount of PMI stays the same as the loan balance shrinks, your effective interest rate goes up (e.g., if you were $16850 away from getting PMI, you'd be paying 3.5%+7.56%).

But, once you put that money into your mortgage, you can't really get it back out without refinancing or selling. So once you pass the point where you'd get rid of PMI via normal payments, your return on that money is only 3.5%. So it still might make sense to pay PMI, depending on how long you expect to be in the house, expected rate of returns on your investments, etc.

Hi, can you check my numbers for a similar situation?

Purchase price: $350,000
3.5% down, $12,250
Balance: $337,750
Interest rate: 4%
PMI: $240/month

350,000*0.8=280,000 <---this is what you need to be at to get rid of PMI

337,750-280,000=57,650 <---this is the amount that you're paying PMI on

240*12=2,880 <---this is the amount of PMI you're paying per year

2,880/57,650=.0499  <---this is the PMI expressed as a proportion of the amount you're paying PMI on

So I'm effectively paying 4.0%+5.00%= 9% to borrow that $57,650

Does this seem right?

boarder42, feel free to weigh in here

kinda. 

its 9% on 57650 but you have to add in the rest of the loan to see your interest rate really on that dollar since its going towards the big pool.  so you should be weighting each portion to find your true rate.

so 57650 is at 9% <-- this number will increase as you get closer to paying off PMI. 

and 280k is at 4%

so of your total loan 9% represents 57650/337750 or 17.1%
and 4% represents 280k/337750 or 82.9% 

so when equally weighted your effective interest rate on each dollar is really.

9%*17.1%+4%*82.9% = 4.855%

this same math applies to the OPs post.

this is how you account for once a dollar goes in it doesnt come out.

Ebrat

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this is close but not entirely correct you dont just add them together you have to add it as a value of the percent of the total loan making it look worse than what your numbers make it to pay down PMI.

Could you explain this a little more or give an example? My spreadsheets thank you in advance :)

Heart of Tin

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I don't agree with all of this weighting based on the size of the loan.

Looking at Cwadda's numbers, for instance, let's consider a single $150 payment made today towards the principle. Instead of 58 PMI payments, Cwadda would then only have 57 PMI payments. Additionally, at the end of the mortgage in 302 months the final payment would be reduced by $408.42. So, that single $150 payment today resulted in a $240 reduction in liability in 58 months and another $408.42 reduction in liability in 302 months. That's a really good internal payoff (over 13% annualized), and no where close to the 4.9% predicted above.

Edit: And the above is the "worst case scenario" assuming Cwadda keeps the loan for at least 58 months. If Cwadda sold the house at 60 months, then we would weight a $150 payment now against a $240 reduction in liability in 58 months and a $182.54 increase in equity in 60 months (23% annualized internal return!).
« Last Edit: May 22, 2017, 03:05:00 PM by Heart of Tin »

Cwadda

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Quote
9%*17.1%+4%*82.9% = 4.855%

Ok, this explains the math well on the .85% FHA PMI standards (you get hit with .85 points for a 3.5% downpayment).

However this is also an investment property and covers the PITI + PMI in full. So do I pay down the mortgage early to get out of PMI?

boarder42

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this is close but not entirely correct you dont just add them together you have to add it as a value of the percent of the total loan making it look worse than what your numbers make it to pay down PMI.

Could you explain this a little more or give an example? My spreadsheets thank you in advance :)

See my post to cwadda

boarder42

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Quote
9%*17.1%+4%*82.9% = 4.855%

Ok, this explains the math well on the .85% FHA PMI standards (you get hit with .85 points for a 3.5% downpayment).

However this is also an investment property and covers the PITI + PMI in full. So do I pay down the mortgage early to get out of PMI?

Not if you wouldn't pay down a 4.85% loan.

boarder42

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I don't agree with all of this weighting based on the size of the loan.

Looking at Cwadda's numbers, for instance, let's consider a single $150 payment made today towards the principle. Instead of 58 PMI payments, Cwadda would then only have 57 PMI payments. Additionally, at the end of the mortgage in 302 months the final payment would be reduced by $408.42. So, that single $150 payment today resulted in a $240 reduction in liability in 58 months and another $408.42 reduction in liability in 302 months. That's a really good internal payoff (over 13% annualized), and no where close to the 4.9% predicted above.

Edit: And the above is the "worst case scenario" assuming Cwadda keeps the loan for at least 58 months. If Cwadda sold the house at 60 months, then we would weight a $150 payment now against a $240 reduction in liability in 58 months and a $182.54 increase in equity in 60 months (23% annualized internal return!).

Doing what you're doing is creative math. If it makes you feel better to pay that down then use it. It's just not the correct way to calculate it.

MDM

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Purchase price: $350,000
3.5% down, $12,250
Balance: $337,750
Interest rate: 4%
PMI: $240/month

kinda. 

its 9% on 57650 but you have to add in the rest of the loan to see your interest rate really on that dollar since its going towards the big pool.  so you should be weighting each portion to find your true rate.

so 57650 is at 9% <-- this number will increase as you get closer to paying off PMI. 

and 280k is at 4%

so of your total loan 9% represents 57650/337750 or 17.1%
and 4% represents 280k/337750 or 82.9% 

so when equally weighted your effective interest rate on each dollar is really.

9%*17.1%+4%*82.9% = 4.855%
Another way to look at it:

Without PMI, the monthly payment on a 30 year $337750 loan at 4% is $1612.47.  In the first month, the interest charge is $337750 * 4% /12 = $1125.83.  Treating the PMI as interest, the effective rate for the first month is ($1125.83 + $240) / $337750 * 12 = 4.853%, the same (to ~3 sig. figs.) as boarder42's number.

By the 13th payment, as the remaining balance and thus the non-PMI interest amounts change, a similar calculation gives ($1106.01 + $240) / $331802.09 * 12 = 4.868%.  The percentage increases slowly over the years....

The annualized ROI for ridding oneself of PMI is $240 * 12 / (current balance - $280000).  At the start of the loan, that is $240 * 12 / ($337750 - $280000) = 4.99%.

By the 13th payment, a similar calculation gives $240 * 12 / ($331802.09 - $280000) = 5.56%.  This percentage will also increase as the remaining balance gets closer to the PMI cutoff.

boarder42

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Purchase price: $350,000
3.5% down, $12,250
Balance: $337,750
Interest rate: 4%
PMI: $240/month

kinda. 

its 9% on 57650 but you have to add in the rest of the loan to see your interest rate really on that dollar since its going towards the big pool.  so you should be weighting each portion to find your true rate.

so 57650 is at 9% <-- this number will increase as you get closer to paying off PMI. 

and 280k is at 4%

so of your total loan 9% represents 57650/337750 or 17.1%
and 4% represents 280k/337750 or 82.9% 

so when equally weighted your effective interest rate on each dollar is really.

9%*17.1%+4%*82.9% = 4.855%
Another way to look at it:

Without PMI, the monthly payment on a 30 year $337750 loan at 4% is $1612.47.  In the first month, the interest charge is $337750 * 4% /12 = $1125.83.  Treating the PMI as interest, the effective rate for the first month is ($1125.83 + $240) / $337750 * 12 = 4.853%, the same (to ~3 sig. figs.) as boarder42's number.

By the 13th payment, as the remaining balance and thus the non-PMI interest amounts change, a similar calculation gives ($1106.01 + $240) / $331802.09 * 12 = 4.868%.  The percentage increases slowly over the years....

The annualized ROI for ridding oneself of PMI is $240 * 12 / (current balance - $280000).  At the start of the loan, that is $240 * 12 / ($337750 - $280000) = 4.99%.

By the 13th payment, a similar calculation gives $240 * 12 / ($331802.09 - $280000) = 5.56%.  This percentage will also increase as the remaining balance gets closer to the PMI cutoff.

thanks for this that is the easier math way for people to understand it.

Bracken_Joy

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Haha, yep, MDM strikes again! I was getting pretty confused there for a bit.

MDM, you seriously have a gift for this stuff. Thanks!

Cwadda

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Thank you!

boarder42

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Haha, yep, MDM strikes again! I was getting pretty confused there for a bit.

MDM, you seriously have a gift for this stuff. Thanks!

same math just done differently to arrive at the same answer.  i've done it that way before but liked how someone presented it this way.  in the future i may show both. 

MDM

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KungfuRabbit

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You can also do upgrades to the house.

My buddy wanted to drop PMI and he had an non-bedroom room in the basement because there was no egress window. 2-weekends later it had an egress window, became a 4-bedroom house, and appraisal went up enough to get rid of PMI.

That's a fairly unique situation though, simpler and more common new house projects (painting, new tile, etc) won't change the appraisal much.

boarder42

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You can also do upgrades to the house.

My buddy wanted to drop PMI and he had an non-bedroom room in the basement because there was no egress window. 2-weekends later it had an egress window, became a 4-bedroom house, and appraisal went up enough to get rid of PMI.

That's a fairly unique situation though, simpler and more common new house projects (painting, new tile, etc) won't change the appraisal much.

or just buy a house under market value.  this works also.  you typically have to REFI to get rid of PMI either of these ways though.  You cant just take an appraisal to the bank and say drop my PMI suckers

Cwadda

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My $337k loan unfortunately has PMI for life. The only way to get rid of it is by refinancing. But I'm not buying it under market value and would have to come up with a lot of cash to get rid of PMI. It cash flows quite a bit though, so I'm going to stick to minimum payments at least for the first year.

Ebrat

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this is close but not entirely correct you dont just add them together you have to add it as a value of the percent of the total loan making it look worse than what your numbers make it to pay down PMI.

Could you explain this a little more or give an example? My spreadsheets thank you in advance :)

See my post to cwadda

Thanks, looks like we cross-posted.

So here's my question after mulling over the math for a while. I can see how weighting the interest rates gives you your overall effective rate. But you say, "you have to add in the rest of the loan to see your interest rate really on that dollar since its going towards the big pool." I would see it as the dollar going toward the PMI portion, since every dollar in principal you pay gets you $1 closer to getting rid of PMI.

I guess it depends on how you look at it and your time horizon. Really, at the point in time when you pay it, that extra dollar only saves you the mortgage interest (and in fact increases your effective rate) because the PMI sticks around until you're under 80%. So the rate you earn on the extra principal payments would depend on 1) your PMI payment, 2) your mortgage rate, 3) how long it will take you to get rid of PMI (with and without extra payments), and 4) how long you plan to keep the mortgage. Setting up a spreadsheet with your extra payment amounts, etc. as someone described above would be the most accurate way to figure out what makes sense for a particular situation.

boarder42

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this is close but not entirely correct you dont just add them together you have to add it as a value of the percent of the total loan making it look worse than what your numbers make it to pay down PMI.

Could you explain this a little more or give an example? My spreadsheets thank you in advance :)

See my post to cwadda

Thanks, looks like we cross-posted.

So here's my question after mulling over the math for a while. I can see how weighting the interest rates gives you your overall effective rate. But you say, "you have to add in the rest of the loan to see your interest rate really on that dollar since its going towards the big pool." I would see it as the dollar going toward the PMI portion, since every dollar in principal you pay gets you $1 closer to getting rid of PMI.

I guess it depends on how you look at it and your time horizon. Really, at the point in time when you pay it, that extra dollar only saves you the mortgage interest (and in fact increases your effective rate) because the PMI sticks around until you're under 80%. So the rate you earn on the extra principal payments would depend on 1) your PMI payment, 2) your mortgage rate, 3) how long it will take you to get rid of PMI (with and without extra payments), and 4) how long you plan to keep the mortgage. Setting up a spreadsheet with your extra payment amounts, etc. as someone described above would be the most accurate way to figure out what makes sense for a particular situation.

see MDM's post above it will likely simplify the math and make it easier for you to understand b/c the length of the loan is not relevant.