### Author Topic: Calling all math wizards out there ...  (Read 4450 times)

#### Melisande

• Bristles
• Posts: 271
##### Calling all math wizards out there ...
« on: June 07, 2016, 11:33:03 AM »
OK, I'm not sure this is in the correct sub-forum, but what I have is essentially a math -- interest rate calculation question -- that I just don't seem to be able to think through and I associate investments discussions with math, so ....

Question: If you pay a large, lump sum (say \$20,000) towards the principle on a loan (say at 3.3%, since this is what our mortgage is at) will you save exactly the same amount of money as you would earn over the same period of time (say 10 years) as you would if you invested that money in a hypothetical bond that had a 3.3% interest rate?

If there is no difference whatsoever in the \$ amount saved or earned (let's not get into taxes and other issues just to keep the calculation simple), would this still be the case if 5 years into the term, we added a second \$20,000 towards paying of the principle on a loan or, alternatively, again invested \$20,000 in a hypothetical bond again with a 3.3% interest rate?

Intuitively, I'd say there was no difference, because it's a 3.3% interest rate either way. However, is there something I'm not seeing here?

#### CmFtns

• Pencil Stache
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• Age: 31
• Location: Melbourne, Fl
##### Re: Calling all math wizards out there ...
« Reply #1 on: June 07, 2016, 11:38:50 AM »
yes paying a 20k principle payment on the 3.3% mortgage would yield exactly the same result as if you put \$20k in an investment that made 3.3% interest and had no fees.

There is a difference and that is that the 3.3% savings from that mortgage principle payment is absolutely guaranteed and there is some value in guaranteed returns... I would absolutely make a mortgage payment 3.3% interest if my only other investment option was a fund with an expected return of 3.3% that was not guaranteed.

It would also be the same scenario 5 years down the road and will always be the same calculation as long as the day you make the payment on your mortgage would be the same day that you made the other investment.

My opinion is that if you have a loan <3% you should probably choose other more promising investments since this is basically keeping up with inflation, if your loan is 3-5% interest then it's kind of a personal choice depending on how risk averse you are, and if the loan is > 5% interest you should probably pay it off aggressively.
« Last Edit: June 07, 2016, 11:45:25 AM by comfyfutons »

#### Melisande

• Bristles
• Posts: 271
##### Re: Calling all math wizards out there ...
« Reply #2 on: June 07, 2016, 03:27:48 PM »
Thanks! Just making sure before I take the \$\$\$ to the bank this week for the mortgage principle paydown.

#### CmFtns

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##### Re: Calling all math wizards out there ...
« Reply #3 on: June 07, 2016, 03:33:43 PM »
Thanks! Just making sure before I take the \$\$\$ to the bank this week for the mortgage principle paydown.

Just wondering... Why do you want to make a large principle payment with such a low interest rate on your mortgage?

#### Shor

• Bristles
• Posts: 480
• Location: Orange County, CA, USA
##### Re: Calling all math wizards out there ...
« Reply #4 on: June 07, 2016, 03:56:36 PM »
Consider the following scenario:
Make payments early -> Lose job -> Go from 80% Equity to nothing when your house gets repossessed
Save extra funds as investments -> Lose job -> Withdraw investments as needed as you look for a new job (hopefully in the next [3] years you find even a low wage job to cover the expenses)

People that lost their shirt in the housing market followed path 1, but had no extra payments and lived life with no buffer and lots of equity. Doesn't matter if you don't pay it off in the end.
People that invested and saved and didn't panic in the crash were able to make ends meet. Sure, they might have taken some investment losses when selling off in a downturn, but they survived, and most of their investment recovered / grew after the bounceback.

#### CmFtns

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##### Re: Calling all math wizards out there ...
« Reply #5 on: June 07, 2016, 04:34:46 PM »
This is a really complicated issue Melisande, I don't think you should rush to a decision without considering all the options.

For Example Consider This: The average inflation rate has been around 3.2%  and your mortgage APR is 3.3% so the total money you pay toward your mortgage will probably be very close to whatever the purchase price was in inflation adjusted dollars if you only make the required payments over 30 years.

#### Heckler

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• Posts: 1411
##### Re: Calling all math wizards out there ...
« Reply #6 on: June 07, 2016, 04:35:11 PM »
Or, consider this alternative that was real life for us.

Pay down mortgage, while also investing the standard 6% of pay retirement plan.  Pay down extra on the mortgage. Lose job, get severance, find new job.

Pay down more mortgage with 75% of your bonuses and raises.  Continue to save 6% for retirement.  Lose job again, get severance, find new job.  Put portion of severance to mortgage.  Lose yet another job, more severance and find another job.  Keep investing 6%, and don't even notice there was a stock market crash in 2008.  Your ignorance is bliss.

Thirteen years later, realize you can burn your mortgage and do so.  Look at your  retirement savings and realize it adds up to 1/5 of a million if you consolidate and learn how you can reduce fees.   Now take the huge ex-mortgage payment and start investing it smartly.   Start planning your Fuck You date.
« Last Edit: June 07, 2016, 04:37:20 PM by Heckler »

#### CmFtns

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##### Re: Calling all math wizards out there ...
« Reply #7 on: June 07, 2016, 04:42:24 PM »
Or, consider this alternative that was real life for us.

Pay down mortgage, while also investing the standard 6% of pay retirement plan.  Pay down extra on the mortgage. Lose job, get severance, find new job.

Pay down more mortgage with 75% of your bonuses and raises.  Continue to save 6% for retirement.  Lose job again, get severance, find new job.  Put portion of severance to mortgage.  Lose yet another job, more severance and find another job.  Keep investing 6%, and dint even notice there was a stock market crash in 2008.  Your ignorance is bliss.

Thirteen years later, realize you can burn your mortgage and do so.  Look at your  retirement savings and realize it adds up to 1/5 of a million if you consolidate and learn how you can reduce fees.   Now take the huge ex-mortgage payment and start investing smartly.   Start planning your Fuck You date.

Heckler, While that path worked for you it was not the most efficient path... It was a conservative path but this scenario would have you better off:

Pay minimum on mortgage for 13 years
Consistently put all those extra mortgage payments into investments instead and never look at stock market
13 years later realize that you have enough investments to pay off mortgage... and even after you do that you still have much more than 1/5 million left over.

#### Chris-93AUS

• Posts: 23
• Age: 2017
• Location: Tasmania, Australia
##### Re: Calling all math wizards out there ...
« Reply #8 on: June 07, 2016, 05:19:33 PM »
Lets not forget that you are taxed on the income from the bond. Mortgage repayment is the way to go IMHO.

#### solon

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• Location: CO
##### Re: Calling all math wizards out there ...
« Reply #9 on: June 07, 2016, 05:27:25 PM »
Lets not forget that you are taxed on the income from the bond. Mortgage repayment is the way to go IMHO.

Hey! You can't be 2011! That's MY age!

#### Melisande

• Bristles
• Posts: 271
##### Re: Calling all math wizards out there ...
« Reply #10 on: June 07, 2016, 08:12:56 PM »
Thanks for all the responses. I already have a thread about whether or not we should actually pay off a 3.3% mortgage in the "Ask a Mustachian" forum. I answered a bunch of questions there about our financial situation and wound up either getting the thumbs up or at least a neutral response from most posters.

It's kind of a complicated situation, but long story short: our finances are in really good shape (my husband could retire now if he wanted to); we both want to pay off the mortgage (for different reasons, one of them being that it is a joint investment instead of only being in my husband's name) and I am just not convinced that we will be seeng that much growth in the stock market over the next five years or so (the time during which we will be paying off the mortgage), so my hunch is that the opportunity cost of paying it off won't be that great.
« Last Edit: June 07, 2016, 08:15:57 PM by Melisande »

#### MDM

• Senior Mustachian
• Posts: 10930
##### Re: Calling all math wizards out there ...
« Reply #11 on: June 07, 2016, 08:24:00 PM »
...I am just not convinced that we will be seeng that much growth in the stock market over the next five years or so (the time during which we will be paying off the mortgage), so my hunch is that the opportunity cost of paying it off won't be that great.
That is a rational reason.  Whether it is correct or not will be known in the next five years or so. ;)

#### MustacheAndaHalf

• Walrus Stache
• Posts: 5195
##### Re: Calling all math wizards out there ...
« Reply #12 on: June 07, 2016, 11:28:29 PM »
Wanted to build on what someone else said, regarding taxes.  Let's take the \$20k at 3.3% interest rate, and assume you're in the median 25% tax bracket.

Think of the mortgage as a negative bond, like \$-20k where the 3.3% interest rate is what you pay.  But mortgages get a tax deduction on interest: the IRS shares in making the payments with you.  So the 3.3% interest gets 1/4th shared with the IRS and becomes roughly 2.5%.  But a bond is the same thing in reverse!  You have \$20k earning 3.3%, and this time the IRS wants a cut which brings you down to 2.5% after taxes.  In both cases, 3.3% is worth 2.5% after taxes.

\$-20k @ 3.3% interest, IRS shares cost = losing 2.5% / year on \$-20k
\$20k @ 3.3% interest, IRS taxes it = gaining 2.5% / year on \$20k
« Last Edit: June 07, 2016, 11:32:02 PM by MustacheAndaHalf »

#### Melisande

• Bristles
• Posts: 271
##### Re: Calling all math wizards out there ...
« Reply #13 on: June 08, 2016, 04:46:24 AM »
Wanted to build on what someone else said, regarding taxes.  Let's take the \$20k at 3.3% interest rate, and assume you're in the median 25% tax bracket.

Think of the mortgage as a negative bond, like \$-20k where the 3.3% interest rate is what you pay.  But mortgages get a tax deduction on interest: the IRS shares in making the payments with you.  So the 3.3% interest gets 1/4th shared with the IRS and becomes roughly 2.5%.  But a bond is the same thing in reverse!  You have \$20k earning 3.3%, and this time the IRS wants a cut which brings you down to 2.5% after taxes.  In both cases, 3.3% is worth 2.5% after taxes.

\$-20k @ 3.3% interest, IRS shares cost = losing 2.5% / year on \$-20k
\$20k @ 3.3% interest, IRS taxes it = gaining 2.5% / year on \$20k

You are right in general and I see your point. But last year, for the first time ever, we had so few deductions that we just wound up using the standard deduction anyway. In other words, although millions of Americans get a tax break on their mortgage interest, we did not. I also do not think that is going to change in the next 5 years.

#### MustacheAndaHalf

• Walrus Stache
• Posts: 5195
##### Re: Calling all math wizards out there ...
« Reply #14 on: June 08, 2016, 09:45:06 AM »
...
Think of the mortgage as a negative bond, like \$-20k where the 3.3% interest rate is what you pay.  But mortgages get a tax deduction on interest: the IRS shares in making the payments with you.  So the 3.3% interest gets 1/4th shared with the IRS and becomes roughly 2.5%.
...
You are right in general and I see your point. But last year, for the first time ever, we had so few deductions that we just wound up using the standard deduction anyway. In other words, although millions of Americans get a tax break on their mortgage interest, we did not. I also do not think that is going to change in the next 5 years.
That's vital information, and makes the case for paying off what you can even stronger.  Vanguard's Total Bond Market has a 2.1% yield, or about 1.5% at the median tax bracket.  Compare that to a mortgage at 3.3% interest with no tax benefit (standard deduction).  Essentially, you have an easy way to make 3.3% interest while everyone else earns 1.5% interest.  So that strengthens the case to pay off part of the mortgage.

#### Heckler

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• Posts: 1411
##### Re: Calling all math wizards out there ...
« Reply #15 on: June 08, 2016, 09:55:28 AM »

Heckler, While that path worked for you it was not the most efficient path... It was a conservative path but this scenario would have you better off:

Easy to say in hindsight, but tough to call when your investments (high cost mutual funds at the time) total value stays flat even though you're contributing off every pay.  That was my experience, and I'm happy I didn't piss away more in fees.  Keep in mind, online investing in low cost index funds wasn't as easily figured out 15 years ago as it is now.

#### CmFtns

• Pencil Stache
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• Location: Melbourne, Fl
##### Re: Calling all math wizards out there ...
« Reply #16 on: June 08, 2016, 10:05:55 AM »

Heckler, While that path worked for you it was not the most efficient path... It was a conservative path but this scenario would have you better off:

Easy to say in hindsight, but tough to call when your investments (high cost mutual funds at the time) total value stays flat even though you're contributing off every pay.  That was my experience, and I'm happy I didn't piss away more in fees.  Keep in mind, online investing in low cost index funds wasn't as easily figured out 15 years ago as it is now.

I guess what I'm saying is not that you should have done it differently back then because your right... it wasn't as easy without internet resources... What I am trying to get at is that now that we have easy access to the vast knowledge of the internet and easy access to low cost index funds why choose the route you took 15 years ago again for people starting out?

I hold a mortgage at 3.875% and I choose to fully invest all my savings vs mortgage payback. I asked myself "Do I believe US Equities will grow at a rate greater than 3.875% over the next 30 years?"... I think this is a pretty good thing to bet on. Also, if I fall on hard times then I have the option to pull on investments and keep paying my mortgage. If I dumped all my money into my mortgage and I fall on hard times then I am still responsible for that payment every month even though I paid down tons of principle.
« Last Edit: June 08, 2016, 10:08:12 AM by CmFtns »