How does this math makes sense?

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 Joined: Sun Aug 25, 2019 10:12 am
How does this math makes sense?
Wife and I are preparing to buy a house. I'm running posthouse budget models and what I'm concluding is whether I put $100K extra down vs invest it at an assumption rate of 5%, the remaining monthly cash after bills/expenses/etc is the same across the scenarios.
For example, let's say we have $1.3M for a down payment.
If I put $1.0M down and then invest the remaining $300K with a conservative 5% growth YoY assumption, my monthly cash remaining after bills/expenses/retirement/etc equals the same amount as if I put $1.1M down and investing $200K, or $1.2M down and investing $100K, etc.
Additionally, if I just put all $1.3M down, there is only about a $200 different between this scenario and the ones above, but in the ones above, I would have $300/$200/$100K of cash on hand for emergencies where the $1.3M down would be stuck in the house.
So in short, is it just a coincidence that the math worked out this way or am I missing something here to be considered? Which scenario should I be taking if this is the case? I would think putting the $1M down, investing the $300K?
For example, let's say we have $1.3M for a down payment.
If I put $1.0M down and then invest the remaining $300K with a conservative 5% growth YoY assumption, my monthly cash remaining after bills/expenses/retirement/etc equals the same amount as if I put $1.1M down and investing $200K, or $1.2M down and investing $100K, etc.
Additionally, if I just put all $1.3M down, there is only about a $200 different between this scenario and the ones above, but in the ones above, I would have $300/$200/$100K of cash on hand for emergencies where the $1.3M down would be stuck in the house.
So in short, is it just a coincidence that the math worked out this way or am I missing something here to be considered? Which scenario should I be taking if this is the case? I would think putting the $1M down, investing the $300K?

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Re: How does this math makes sense?
You seem to be doing something wrong. The more you put down, the lower your monthly mortgage payment should be as you’ll be paying less interest.
As to what will ultimately be better, it depends on taxes and your investment return. If you get 5% you’ll probably come out ahead if it’s a taxefficient investment (paying towards mortgage gets you an aftertax return at the loan rate). But the market makes no promises on returns.
As to what will ultimately be better, it depends on taxes and your investment return. If you get 5% you’ll probably come out ahead if it’s a taxefficient investment (paying towards mortgage gets you an aftertax return at the loan rate). But the market makes no promises on returns.

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Re: How does this math makes sense?
If you assume 5% vs a 4% mortgage on $100300k you shouldn’t expect to see big differences.
Question is, will the market return 5%? 10% or 10% over the next 10 years. Nobody knows.
If you plan to live there for 30+ years, you’ll probably realize closer to 10% on stock investments. Many people don’t stay for 30 years in a house though.
Question is, will the market return 5%? 10% or 10% over the next 10 years. Nobody knows.
If you plan to live there for 30+ years, you’ll probably realize closer to 10% on stock investments. Many people don’t stay for 30 years in a house though.
Re: How does this math makes sense?
As I used to tell my kids when helping with their math homework: if you want help, you need to show your work.socialforums2019 wrote: ↑Fri Feb 14, 2020 8:09 amSo in short, is it just a coincidence that the math worked out this way or am I missing something here to be considered?
Very Stable Genius

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 Joined: Sun Aug 25, 2019 10:12 am
Re: How does this math makes sense?
Haha ok I'll play along. The scenarios below are focused on what's "left over" after all the bills/expense/savings/retirement/additional retirement/529 contributions/emergency funds/etc. are paid and contributions made.JoeRetire wrote: ↑Fri Feb 14, 2020 8:22 amAs I used to tell my kids when helping with their math homework: if you want help, you need to show your work.socialforums2019 wrote: ↑Fri Feb 14, 2020 8:09 amSo in short, is it just a coincidence that the math worked out this way or am I missing something here to be considered?
For simplifying calculations, the investment assumption is just taking the invested amount * .05 (5%) divided by 12 to get a "monthly interest income"
$1.0M Down Scenario with $300K invested
"Left Over": $289
Investment Interest Income: $1,250
"True Left Over": $961
$1.1M Down Scenario with $200K invested
"Left Over": $151
Investment Interest Income: $833
"True Left Over": $984
$1.2M Down Scenario with $100K invested
"Left Over": $629
Investment Interest Income: $416
"True Left Over": $1045
$1.3M Down Scenario with $0 invested
"Left Over": $1106
Investment Interest Income: $0
"True Left Over": $1106
Last edited by socialforums2019 on Sat Feb 15, 2020 8:29 am, edited 2 times in total.
 JupiterJones
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 Location: Nashville, TN
Re: How does this math makes sense?
The math makes some sense, but the assumptions are a bit shaky. As mentioned, you're comparing riskfree "earnings" (100% certain reduction in interest with every extra dollar of down payment) to a nonriskfree investment (maybe you'll get 5%, maybe not).
Assuming you do have an adequatelyfunded emergency fund (that is, you don't need the extra cash on hand for emergencies that you mentioned), why not just put the whole $1.3M down on the house?
If you later change your mind, you can always take a second mortgage out for a few hundred thou and invest away with it. Mathematically, it's about the same as if you withheld that amount from your down payment and invested it on the outset. (But, of course, emotionally/mentally it hits you a bit differently, which is sort of the point.)
Assuming you do have an adequatelyfunded emergency fund (that is, you don't need the extra cash on hand for emergencies that you mentioned), why not just put the whole $1.3M down on the house?
If you later change your mind, you can always take a second mortgage out for a few hundred thou and invest away with it. Mathematically, it's about the same as if you withheld that amount from your down payment and invested it on the outset. (But, of course, emotionally/mentally it hits you a bit differently, which is sort of the point.)
Stay on target...
Re: How does this math makes sense?
We're talking a million plus $$ here for a down payment....
I'm guessing there's lots of other money in the portfolio and income. Is worrying about this really that high on the priority list? Put it all down and keep on saving and investing.
I'm guessing there's lots of other money in the portfolio and income. Is worrying about this really that high on the priority list? Put it all down and keep on saving and investing.
Re: How does this math makes sense?
+1. OP is obviously doing very well if he/she can put down a million dollars as downpayment. It is really six of one, half a dozen of the other. Either way OP will be fine.
Re: How does this math makes sense?
When I do that, kid takes umbrage and stomps off. Oh well, my kid my issueJoeRetire wrote: ↑Fri Feb 14, 2020 8:22 amAs I used to tell my kids when helping with their math homework: if you want help, you need to show your work.socialforums2019 wrote: ↑Fri Feb 14, 2020 8:09 amSo in short, is it just a coincidence that the math worked out this way or am I missing something here to be considered?
At least, OP came back with some numbers
Re: How does this math makes sense?
Something does not make sense. For one, I don't understand "Left Over" and how it is calculated. Secondly, I don't understand how the Left Over is identical for $1.0M down and for $1.3M down.socialforums2019 wrote: ↑Fri Feb 14, 2020 9:31 amHaha ok I'll play along. The scenarios below are focused on what's "left over" after all the bills/expense/savings/retirement/additional retirement/529 contributions/emergency funds/etc. are paid and contributions made.JoeRetire wrote: ↑Fri Feb 14, 2020 8:22 amAs I used to tell my kids when helping with their math homework: if you want help, you need to show your work.socialforums2019 wrote: ↑Fri Feb 14, 2020 8:09 amSo in short, is it just a coincidence that the math worked out this way or am I missing something here to be considered?
For simplifying calculations, the investment assumption is just taking the invested amount * .05 (5%) divided by 12 to get a "monthly interest income"
$1.0M Down Scenario with $300K invested
"Left Over": $289
Investment Interest Income: $1,250
"True Left Over": $961
$1.1M Down Scenario with $200K invested
"Left Over": $151
Investment Interest Income: $833
"True Left Over": $984
$1.2M Down Scenario with $100K invested
"Left Over": $629
Investment Interest Income: $416
"True Left Over": $1045
$1.3M Down Scenario with $0 invested
"Left Over": $289
Investment Interest Income: $0
"True Left Over": $1106
That said, if you take a  say  $100k loan at 5% and put your $100k in the bank earning 5%, you will be quits at any future point of reference. And that will be equivalent of doing neither of those actions OR doubling down, i.e., $200k loan and depositing $200k in the bank. Is that what you are trying to demonstrate?
Re: How does this math makes sense?
This "left over/true left over" focus is confusing.socialforums2019 wrote: ↑Fri Feb 14, 2020 9:31 amHaha ok I'll play along. The scenarios below are focused on what's "left over" after all the bills/expense/savings/retirement/additional retirement/529 contributions/emergency funds/etc. are paid and contributions made.
For simplifying calculations, the investment assumption is just taking the invested amount * .05 (5%) divided by 12 to get a "monthly interest income"
What does a negative "left over" amount mean?$1.0M Down Scenario with $300K invested
"Left Over": $289
$1.3M Down Scenario with $0 invested
"Left Over": $289
Is this your math error?
How could "left over" be the same in both scenarios?
Wouldn't it have been simpler just to list your actual numbers for loan amount, down payment amount, loan rate, presumed investment rate, and assumed inflation rate?
Very Stable Genius

 Posts: 33
 Joined: Sun Aug 25, 2019 10:12 am
Re: How does this math makes sense?
"Left over" is basically left over savings. How much money I have left over at the end of the month after paying and/or allocating money to the budget such as the below:
Retirement fund contributions (pre and posttax contributions)
529 fund contributions
Basic monthly expenses (e.g. groceries, cell phone, internet, electricity, etc.)
"Fun Money" (e.g. Things such as personal funds, date night fund, shopping fund, etc.)
Monthly allocation for one time annual payments (e.g. property tax, car registration, etc)
Allocation of emergency money (e.g. Home maintenance, auto maintenance, etc.)
So in the case that there is a initial "negative left over" amount, that means that I am losing money each month out of my checking account, but if you consider the assumed investment interest income, then its actually positive.
I made a mistake on the numbers for the $1.3M down situation. That should be $1.1K "left over" straight up. I'll update the numbers
Retirement fund contributions (pre and posttax contributions)
529 fund contributions
Basic monthly expenses (e.g. groceries, cell phone, internet, electricity, etc.)
"Fun Money" (e.g. Things such as personal funds, date night fund, shopping fund, etc.)
Monthly allocation for one time annual payments (e.g. property tax, car registration, etc)
Allocation of emergency money (e.g. Home maintenance, auto maintenance, etc.)
So in the case that there is a initial "negative left over" amount, that means that I am losing money each month out of my checking account, but if you consider the assumed investment interest income, then its actually positive.
I made a mistake on the numbers for the $1.3M down situation. That should be $1.1K "left over" straight up. I'll update the numbers
Re: How does this math makes sense?
You are making this more complicated than needed. The return of making additional principle payments on a mortgage is simply the interest rate of the loan. Put simply if you compare the interest rate of the loan to the return of your investment it would show which would come out ahead. However, return needs to be adjusted for risk. Paying off a mortgage is a guaranteed return and is best compared to the return of your fixed income assets (after tax).