## How does this math makes sense?

Non-investing personal finance issues including insurance, credit, real estate, taxes, employment and legal issues such as trusts and wills
Topic Author
socialforums2019
Posts: 33
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 post-house 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?

MotoTrojan
Posts: 8156
Joined: Wed Feb 01, 2017 8:39 pm

### 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 tax-efficient investment (paying towards mortgage gets you an after-tax return at the loan rate). But the market makes no promises on returns.

BanquetBeer
Posts: 433
Joined: Thu Jul 13, 2017 5:57 pm

### Re: How does this math makes sense?

If you assume 5% vs a 4% mortgage on \$100-300k 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.

JoeRetire
Posts: 4757
Joined: Tue Jan 16, 2018 2:44 pm

### Re: How does this math makes sense?

socialforums2019 wrote:
Fri Feb 14, 2020 8:09 am
So in short, is it just a coincidence that the math worked out this way or am I missing something here to be considered?
As I used to tell my kids when helping with their math homework: if you want help, you need to show your work.
Very Stable Genius

Topic Author
socialforums2019
Posts: 33
Joined: Sun Aug 25, 2019 10:12 am

### Re: How does this math makes sense?

JoeRetire wrote:
Fri Feb 14, 2020 8:22 am
socialforums2019 wrote:
Fri Feb 14, 2020 8:09 am
So in short, is it just a coincidence that the math worked out this way or am I missing something here to be considered?
As I used to tell my kids when helping with their math homework: if you want help, you need to show your work.
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.

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
Posts: 2823
Joined: Tue Aug 24, 2010 3:25 pm
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 risk-free "earnings" (100% certain reduction in interest with every extra dollar of down payment) to a non-risk-free investment (maybe you'll get 5%, maybe not).

Assuming you do have an adequately-funded 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...

chevca
Posts: 3114
Joined: Wed Jul 26, 2017 11:22 am

### 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.

student
Posts: 4492
Joined: Fri Apr 03, 2015 6:58 am

### Re: How does this math makes sense?

chevca wrote:
Fri Feb 14, 2020 9:58 am
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.
+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.

Posts: 2619
Joined: Thu Jun 27, 2013 2:15 pm

### Re: How does this math makes sense?

JoeRetire wrote:
Fri Feb 14, 2020 8:22 am
socialforums2019 wrote:
Fri Feb 14, 2020 8:09 am
So in short, is it just a coincidence that the math worked out this way or am I missing something here to be considered?
As I used to tell my kids when helping with their math homework: if you want help, you need to show your work.
When I do that, kid takes umbrage and stomps off. Oh well, my kid my issue

At least, OP came back with some numbers

Posts: 2619
Joined: Thu Jun 27, 2013 2:15 pm

### Re: How does this math makes sense?

socialforums2019 wrote:
Fri Feb 14, 2020 9:31 am
JoeRetire wrote:
Fri Feb 14, 2020 8:22 am
socialforums2019 wrote:
Fri Feb 14, 2020 8:09 am
So in short, is it just a coincidence that the math worked out this way or am I missing something here to be considered?
As I used to tell my kids when helping with their math homework: if you want help, you need to show your work.
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.

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
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.

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?

JoeRetire
Posts: 4757
Joined: Tue Jan 16, 2018 2:44 pm

### Re: How does this math makes sense?

socialforums2019 wrote:
Fri Feb 14, 2020 9:31 am
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.

For simplifying calculations, the investment assumption is just taking the invested amount * .05 (5%) divided by 12 to get a "monthly interest income"
This "left over/true left over" focus is confusing.
\$1.0M Down Scenario with \$300K invested
"Left Over": -\$289

\$1.3M Down Scenario with \$0 invested
"Left Over": -\$289
What does a negative "left over" amount mean?
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

Topic Author
socialforums2019
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 post-tax 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

Nate79
Posts: 5414
Joined: Thu Aug 11, 2016 6:24 pm
Location: Delaware

### 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).