# Math Behind Buying a House with Calculations

This is a follow-up question to Math Behind Buying a House

As many answers pointed out, my calculations in the previous question were flawed. What do you think about the updated calculations below and my conclusions? (I used http://www.amortization-calc.com/ to generate the amortization schedule)

``````Price for the House: \$225,000
Down Payment (5%): \$11,500
Loan Term: 30 yrs
Interest Rate: 4.5%

At the end of 3 years:

Total Interest:             9537+9379+9213 = 28,130
Total Insurance (on avg)    3000+3000+3000 = 9,000
Total Tax (on avg)          3200+3200+3200 = 9,600
Closing costs (selling)     225,000 * 8%   = 18,000

Total Principal:            3444+3602+3768 = 10,814

Total unrecoverable expenses: interest + insurance + tax + closing = \$64,730
Equity  :           principal                                      = \$10,814

Considering 0 appreciation, and no maintenance costs (to simplify the math)
for the house, we will be spending \$64,730 that is not recoverable.
Therefore, I will be better off if I rent a house below \$1,800/month
(\$64,730/36)
``````
• "no maintenance costs for the house" that is not realistic at all. Unless you buy a house with no lawn and no major appliances (air conditioner, hot water heater, etc.). that makes it even more reasonable to rent rather than buy. – D Stanley Aug 29 '17 at 18:21
• There's a small impact still missing here for the 3 years of investment income you could have accrued on the down payment + principal. On ~14k at 7% [assuming average equity returns, arguably similar to the risk taken on by property ownership] * 3 years that equals \$3k using very simple math. However the missing maintenance costs may be a larger impact than this. – Grade 'Eh' Bacon Aug 29 '17 at 18:23
• Your insurance estimate seems ~3x too high (unless factoring in PMI), your tax seems high also, but might be reasonable depending on locale. Also missing is the tax-savings due to mortgage interest, but that won't likely be terribly significant. – Hart CO Aug 29 '17 at 18:27
• @Grade'Eh'Bacon Using "average equity returns" for such a short period is a pretty bold assumption. – xiaomy Aug 29 '17 at 18:59

I haven't verified your amortization numbers, but they're in the right ballpark.

Also bear in mind that when it comes time to sell the house, you may not be able to sell it instantly. You could have a considerable time where you are still paying the mortgage and taxes even though you are not living in the house.

It is rarely worthwhile to buy a house if you know you are likely to move away in less than 3 years.

In general, this is correct, however, there are several points you miss, which make the result different.

• you can deduct the interest from taxes. Depending on your tax situation, you might save 25% or more from the 28000, which is a significant amount (your rent is not tax-deductable).
• the calculation changes significantly when you change the duration. If you are bound to exactly three years, then it might be correct, but if you try the same math for four years, or even for 3 years and one month, you will see it comes out differently, as the one-time buying cost have less impact.
• house prices change, in average they go slightly up. Assuming the average inflation ratio would give a better estimate. However, there is of course the chance that prices go down or increase more. This adds a risk as well as a potential gain, and makes the overall result more difficult to predict. Rent prices change, you also should estimate them to go up at least with inflation.
• Note that applying inflation ratio to both of them does not even out, but adds to the same direction - buying becomes a better economic value / comparable starting rent will be smaller.
• there are smaller side effects of having a mortgage or paying rent to your credit score, etc., which influences what you pay for a car loan, etc. It is very difficult to calculate anything though; so just be aware of it.
• your rent contract could be terminated at an inconvenient time, and you'll have to move. You might be able to make the contract for the full time, but then you are stuck with what might turn out a bad choice (of property or of owner).
• there are non-monetary differences that don't cost you money, but still can be effect you significantly. Many rent contracts nowadays require you to endure full-house video recordings every six months to document the statethe house is in, and disallow you certain usages (like putting hooks in the walls to hang pictures). It depends of course of you contract, but generally, the more valuable the house, the pickier the owners are (and for a good reason).
• this might not apply to you, but many people enjoy the option to customize things in their house or garden; with a rental, this is very restricted, and even if you would be allowed, you lose the value of any additions to the owner.

Regarding the calculation, I find 3000 insurance very high. I pay 1600 for a house double that value, but of course that could be very different depending on location.