### Author Topic: Mortgage Math (Dummies Version)  (Read 440 times)

• Stubble
• Posts: 162
##### Mortgage Math (Dummies Version)
« on: April 15, 2021, 07:23:11 PM »
I am considering moving to the US, and am weighing the pros and cons of renting versus buying once I know the location where I will live a bit better.  I have no interest in buying immediately and will rent for about a year.

I am wondering if my back of the envelope math is right, which then will lead to a conclusion that will help me determine whether to buy or just keep renting indefinitely.

Here's my train of thought.

Houses in the area are going for about USD 1 Million (stupid price, that is generally the bottom of the market).  According to an amortization calculator I found, I get this for the first year (in rounded yearly numbers):

Mortgage payment: \$60,000;
of which, principal is: \$15,600; and
interest is: \$31,080

Another back of the envelope calculation gives me an effective tax rate of 30% (rounded again). This would mean that of my yearly \$60,000:

\$15,600 is my equity build-up
\$31,080 (i.e. 80% of goes up in smoke)

In my mind, if I rent a place for under \$31,080 a year, I would be better off renting instead of buying.  I know this is Heresy for middle class Americans, but is the basic math wrong?

The above assumes that additional costs and benefits of homeownership (transaction costs, insurance, appreciation, maintenance, etc.) and the investment yield of down payment plus the difference between rental and mortgage costs more or less balance out.

On a monthly basis, I know that a house with a \$5,000 mortgage would be nicer than a condo rented for \$2,600.  I am setting that aside for the moment.
« Last Edit: April 15, 2021, 08:41:42 PM by WalkaboutStache »

#### nereo

• Senior Mustachian
• Posts: 14942
• Location: Just south of Canada
##### Re: Mortgage Math (Dummies Version)
« Reply #1 on: April 15, 2021, 07:41:15 PM »
Quote
The above assumes that additional costs and benefits of homeownership (transaction costs, insurance, appreciation, maintenance, etc.) and the investment yield of down payment plus the difference between rental and mortgage costs more or less balance out.

I think that is an erroneous assumption to make.

Overall, I’ve found this to be a very good calculator.

Depending on your assumptions, I’d place you better off renting if you can find a place for under \$3,700/month (or \$44,400/year).
I cannot find any plausible scenario in which you would be better off financially owning a home that expensive if you could rent it for \$31k/year.
Yes, home ownership can be wicked expensive.

Mind you, there are other factors to consider, including whether one can even find the sort of home you are looking for to rent in that particular area.  Rental and Purchase options are often very different, particularly at the higher end of the spectrum.

#### maizefolk

• Walrus Stache
• Posts: 5772
##### Re: Mortgage Math (Dummies Version)
« Reply #2 on: April 15, 2021, 07:50:31 PM »
I'm not sure I'm following your math with regard to effective tax rates, could you expand a bit more on your reasoning?

If you are paying \$60,000/year on a 30 year mortgage with a starting value of \$800,000 (assuming a 20% downpayment, are you in a position to make that?), my back of the envelope math puts you at 45,600/year in combined interest and principal which is a lot higher than the number you are getting (\$15,600 + \$3,700 = \$19,300 combined principal and interest). Might be worth it to double checking either your numbers or assumptions although it could certainly be me who is off.

• Stubble
• Posts: 162
##### Re: Mortgage Math (Dummies Version)
« Reply #3 on: April 15, 2021, 08:44:17 PM »
You are right, @maizefolk!  That number should be 31,080.

For the effective tax rate, I just plugged numbers into a calculator that computed state and federal taxes.

https://smartasset.com/taxes/income-taxes#WsPLXFzW9A

@nereo, I did a trulia search around Dana Point, CA.  Believe it or not, that seems to be closer to the lower end of the spectrum there.  It is shocking.

I had forgotten about the NYT calculator.  It actually spit out an even larger rental number (\$3,800), which would make the quality of the rental even higher.  I can't stomach paying that much in rent.

All of this is largely spitballing things on my end.  There are a couple of other countries where I might end up.  One of the upsides of Covid is this whole work from home thing.

« Last Edit: April 15, 2021, 09:19:03 PM by WalkaboutStache »