## Mortgage Math Including Taxes and Inflation

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Topic Author
tooluser
Posts: 915
Joined: Sat Oct 01, 2011 7:04 pm

### Mortgage Math Including Taxes and Inflation

Is this math correct?

Mortgage Rate (M): 2.375%
Federal Tax Rate (F): 32%
State Tax Rate (S): 9.3%
Inflation rate (I): 4.16%

Effective Mortgage Rate = M * (1 - F - S) - I
= 2.375% * (1 - 32% - 9.3%) - 4.16% = -2.766%

So, assuming all the interest is deductible, on a mortgage of \$150k one would "earn" \$4148.81 on an annual basis. (=\$150k * 2.766%)
This would more than offset the annual interest payments of approximately \$3500.
mervinj7
Posts: 1853
Joined: Thu Mar 27, 2014 3:10 pm

### Re: Mortgage Math Including Taxes and Inflation

tooluser wrote: Sun May 16, 2021 7:16 pm Is this math correct?

Mortgage Rate (M): 2.375%
Federal Tax Rate (F): 32%
State Tax Rate (S): 9.3%
Inflation rate (I): 4.16%

Effective Mortgage Rate = M * (1 - F - S) - I
= 2.375% * (1 - 32% - 9.3%) - 4.16% = -2.766%

So, assuming all the interest is deductible, on a mortgage of \$150k one would "earn" \$4148.81 on an annual basis. (=\$150k * 2.766%)
This would more than offset the annual interest payments of approximately \$3500.
How did you figure on 4.16% for long term inflation?
grok87
Posts: 9613
Joined: Tue Feb 27, 2007 9:00 pm

### Re: Mortgage Math Including Taxes and Inflation

tooluser wrote: Sun May 16, 2021 7:16 pm Is this math correct?

Mortgage Rate (M): 2.375%
Federal Tax Rate (F): 32%
State Tax Rate (S): 9.3%
Inflation rate (I): 4.16%

Effective Mortgage Rate = M * (1 - F - S) - I
= 2.375% * (1 - 32% - 9.3%) - 4.16% = -2.766%

So, assuming all the interest is deductible, on a mortgage of \$150k one would "earn" \$4148.81 on an annual basis. (=\$150k * 2.766%)
This would more than offset the annual interest payments of approximately \$3500.
can you explain the inflation part? i'm not getting it
RIP Mr. Bogle.
Topic Author
tooluser
Posts: 915
Joined: Sat Oct 01, 2011 7:04 pm

### Re: Mortgage Math Including Taxes and Inflation

mervinj7 wrote: Sun May 16, 2021 7:24 pm
tooluser wrote: Sun May 16, 2021 7:16 pm Is this math correct?

Mortgage Rate (M): 2.375%
Federal Tax Rate (F): 32%
State Tax Rate (S): 9.3%
Inflation rate (I): 4.16%

Effective Mortgage Rate = M * (1 - F - S) - I
= 2.375% * (1 - 32% - 9.3%) - 4.16% = -2.766%

So, assuming all the interest is deductible, on a mortgage of \$150k one would "earn" \$4148.81 on an annual basis. (=\$150k * 2.766%)
This would more than offset the annual interest payments of approximately \$3500.
How did you figure on 4.16% for long term inflation?
April 2021 annualized inflation rate per inflationdata.com. I believe that's the same as the government-reported data but I don't know exactly where to look for it at a .gov site. Clearly the inflation rate will vary month to month, but for illustrative purposes I had to pick a number.

For grok87: If the dollars are inflating, then the balance should - in some sense - fall with the inflation rate?
drk
Posts: 2390
Joined: Mon Jul 24, 2017 10:33 pm
Location: Overlooking Elliott Bay

### Re: Mortgage Math Including Taxes and Inflation

tooluser wrote: Sun May 16, 2021 7:28 pm April 2021 annualized inflation rate per inflationdata.com. I believe that's the same as the government-reported data but I don't know exactly where to look for it at a .gov site. Clearly the inflation rate will vary month to month, but for illustrative purposes I had to pick a number.
BLS posts latest numbers here: https://www.bls.gov/cpi/latest-numbers.htm (4.2, which could be rounded from 4.16)
Topic Author
tooluser
Posts: 915
Joined: Sat Oct 01, 2011 7:04 pm

### Re: Mortgage Math Including Taxes and Inflation

drk: Thank you.

Another way to phrase the question:
M*(1-F-S) in the example above = 1.394%
So if the monthly inflation rate is above 1.394%, does the example mortgage generate income (rather than being an expense)?
leeks
Posts: 1109
Joined: Thu Apr 07, 2011 4:33 pm
Location: virginia

### Re: Mortgage Math Including Taxes and Inflation

tooluser wrote: Sun May 16, 2021 7:16 pm Is this math correct?

Mortgage Rate (M): 2.375%
Federal Tax Rate (F): 32%
State Tax Rate (S): 9.3%
Inflation rate (I): 4.16%

Effective Mortgage Rate = M * (1 - F - S) - I
= 2.375% * (1 - 32% - 9.3%) - 4.16% = -2.766%

So, assuming all the interest is deductible, on a mortgage of \$150k one would "earn" \$4148.81 on an annual basis. (=\$150k * 2.766%)
This would more than offset the annual interest payments of approximately \$3500.
Topic Author
tooluser
Posts: 915
Joined: Sat Oct 01, 2011 7:04 pm

### Re: Mortgage Math Including Taxes and Inflation

leeks wrote: Sun May 16, 2021 7:48 pm
tooluser wrote: Sun May 16, 2021 7:16 pm Is this math correct?

Mortgage Rate (M): 2.375%
Federal Tax Rate (F): 32%
State Tax Rate (S): 9.3%
Inflation rate (I): 4.16%

Effective Mortgage Rate = M * (1 - F - S) - I
= 2.375% * (1 - 32% - 9.3%) - 4.16% = -2.766%

So, assuming all the interest is deductible, on a mortgage of \$150k one would "earn" \$4148.81 on an annual basis. (=\$150k * 2.766%)
This would more than offset the annual interest payments of approximately \$3500.
Why not? It's all spelled out.
grok87
Posts: 9613
Joined: Tue Feb 27, 2007 9:00 pm

### Re: Mortgage Math Including Taxes and Inflation

tooluser wrote: Sun May 16, 2021 7:28 pm
mervinj7 wrote: Sun May 16, 2021 7:24 pm
tooluser wrote: Sun May 16, 2021 7:16 pm Is this math correct?

Mortgage Rate (M): 2.375%
Federal Tax Rate (F): 32%
State Tax Rate (S): 9.3%
Inflation rate (I): 4.16%

Effective Mortgage Rate = M * (1 - F - S) - I
= 2.375% * (1 - 32% - 9.3%) - 4.16% = -2.766%

So, assuming all the interest is deductible, on a mortgage of \$150k one would "earn" \$4148.81 on an annual basis. (=\$150k * 2.766%)
This would more than offset the annual interest payments of approximately \$3500.
How did you figure on 4.16% for long term inflation?
April 2021 annualized inflation rate per inflationdata.com. I believe that's the same as the government-reported data but I don't know exactly where to look for it at a .gov site. Clearly the inflation rate will vary month to month, but for illustrative purposes I had to pick a number.

For grok87: If the dollars are inflating, then the balance should - in some sense - fall with the inflation rate?
ah i see. i like the idea.

to make it more precise, you might think in terms of hypothetical cash flows:

1) you buy a house for 100k dollars and take out a mortgage
1) You pay out gross interest of 2.375k during the year
2) you get a tax refund for 2.375k*(32%+9.3%) = \$0.743 k
3) you sell the house 1 year later for 100k*(1+4.16%) =104.16k
4) net result 104.16- 2.375 + 0.743 -100 = 2.528
i.e. a negative interest rate =-2.528%

now this is the same result you already got. but thinking in cash flows and dollars, IMHO, does shed some light:

5) You want to think about house price appreciation not inflation
6) is 2) above correct, i.e. the tax deductibility? Since the standard deduction is \$12.4k and property taxes are limited to \$10k for this level of interest there would be no real deduction even if property tax were \$10k (unlikely for a \$100k property).

cheers,
grok
RIP Mr. Bogle.
leeks
Posts: 1109
Joined: Thu Apr 07, 2011 4:33 pm
Location: virginia

### Re: Mortgage Math Including Taxes and Inflation

Based on grok's interpretation:
1. Is the inflation value meant to be an estimate for the new value of the house?
2. Is the mortgage interest expected to have a tax benefit? In our case, the higher standard deduction (and SALT deduction limit) means our mortgage has no tax impact (as grok noted).
3. How have you considered the ongoing costs - insurance, property tax, maintenance, etc?
4. What is the comparison - renting an equivalent place (with rent increases expected to go up by inflation)?
alex_686
Posts: 8521
Joined: Mon Feb 09, 2015 2:39 pm

### Re: Mortgage Math Including Taxes and Inflation

drk wrote: Sun May 16, 2021 7:38 pm
tooluser wrote: Sun May 16, 2021 7:28 pm April 2021 annualized inflation rate per inflationdata.com. I believe that's the same as the government-reported data but I don't know exactly where to look for it at a .gov site. Clearly the inflation rate will vary month to month, but for illustrative purposes I had to pick a number.
BLS posts latest numbers here: https://www.bls.gov/cpi/latest-numbers.htm (4.2, which could be rounded from 4.16)
Monthly numbers are very noisy, so I would ignore that. One of the better methods is to look at the spread between 10 year treasuries and 10 year TIPS. It is currently around 2.5%.

https://fred.stlouisfed.org/series/T10YIE

Also, these forecasts have huge error margins. I would not round to the nearest 0.1%. Rather, the closest quarter, or 0.25%. And I would be conservative and round down.
Former brokerage operations & mutual fund accountant. I hate risk, which is why I study and embrace it.
drk
Posts: 2390
Joined: Mon Jul 24, 2017 10:33 pm
Location: Overlooking Elliott Bay

### Re: Mortgage Math Including Taxes and Inflation

alex_686 wrote: Mon May 17, 2021 10:04 am Monthly numbers are very noisy, so I would ignore that. One of the better methods is to look at the spread between 10 year treasuries and 10 year TIPS. It is currently around 2.5%.
Note that the OP was just looking for a placeholder value to check the math, not projecting out future inflation.
corn18
Posts: 2233
Joined: Fri May 22, 2015 6:24 am

### Re: Mortgage Math Including Taxes and Inflation

Makes sense to me. I keep things simple since I cannot deduct any interest. My 30 year fixed interest rate is 2.75%. The 10 yr breakeven inflation rate is 2.51%. The real interest rate on my mortgage is 0.24%. If inflation gets above 2.75%, I am making money in real terms.
Last edited by corn18 on Mon May 17, 2021 11:40 am, edited 1 time in total.
Don't do something, just stand there!
Nate79
Posts: 7166
Joined: Thu Aug 11, 2016 6:24 pm
Location: Delaware

### Re: Mortgage Math Including Taxes and Inflation

tooluser wrote: Sun May 16, 2021 7:45 pm drk: Thank you.

Another way to phrase the question:
M*(1-F-S) in the example above = 1.394%
So if the monthly inflation rate is above 1.394%, does the example mortgage generate income (rather than being an expense)?
A mortgage doesn't generate income. Perhaps you should reword the purpose of the calculation. Inflation doesn't pay you anything. It doesnt put money in your pocket.
alex_686
Posts: 8521
Joined: Mon Feb 09, 2015 2:39 pm

### Re: Mortgage Math Including Taxes and Inflation

Nate79 wrote: Mon May 17, 2021 10:46 am So if the monthly inflation rate is above 1.394%, does the example mortgage generate income (rather than being an expense)?
A mortgage doesn't generate income. Perhaps you should reword the purpose of the calculation. Inflation doesn't pay you anything. It doesnt put money in your pocket.
[/quote]

A mortgage is a negative bond. As such, it is always a liability and a expense. It increases leverage and thus risk. Try not paying your mortgage for a couple of months.

That being said, this is very cheap money, in both real and nominal terms.
Former brokerage operations & mutual fund accountant. I hate risk, which is why I study and embrace it.
Ketawa
Posts: 2363
Joined: Mon Aug 22, 2011 1:11 am
Location: DC

### Re: Mortgage Math Including Taxes and Inflation

tooluser wrote: Sun May 16, 2021 7:16 pm Is this math correct?

Mortgage Rate (M): 2.375%
Federal Tax Rate (F): 32%
State Tax Rate (S): 9.3%
Inflation rate (I): 4.16%

Effective Mortgage Rate = M * (1 - F - S) - I
= 2.375% * (1 - 32% - 9.3%) - 4.16% = -2.766%

So, assuming all the interest is deductible, on a mortgage of \$150k one would "earn" \$4148.81 on an annual basis. (=\$150k * 2.766%)
This would more than offset the annual interest payments of approximately \$3500.
4.16% is basically a 1-month aberration due to the temporary decline in prices last year at the start of the pandemic. However, ignoring that...

This wouldn't calculate an "effective mortgage rate". One could call it a "real mortgage rate", I suppose.

However, that doesn't mean you would be making money off your mortgage. You have to consider opportunity cost. The cost of your mortgage is really the spread between what you are paying and what you can make in a similar fixed income investment, which should be Treasuries (paying off your mortgage is risk free to you, just as a Treasury is risk free to you). The inflation rate is irrelevant and cancels out.

Nominal Investment Rate (N): Treasuries are all below 2.375%
Real Mortgage Rate = M * (1 - F - S) - I
Real Investment Rate = N * (1 - F - S) - I
Opportunity Cost = Real Mortgage Rate - Real Investment Rate = (M - R) * Taxes > 0
IMO
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Joined: Fri May 05, 2017 6:01 pm

### Re: Mortgage Math Including Taxes and Inflation

Your mortgage would have to still be tax deductible to you. If it is, then you still have to factor in one must account for the standard deduction (currently \$24,800 married couple) that you get regardless of having a mortgage. Even if it's deductible, there can be a point where it may be better to start claiming the standard deduction vs itemizing it (when interest/state taxes are less than the standard deduction).

But isn't it really more accurate to adjust your mortgage rate UP in a sense? One is typically paying the mortgage/interest in after tax dollars (much less common now for it to be tax deductible)? Seems it's common to say stock market returned "x" and that doesn't account for typically for taxes one would have to pay on that stock market return at some point (let alone to account for inflation "cost") Then with mortgages, we say it only cost us "y" amount in interest, but that interest is paid typically in real time with after tax dollars. Is it more correct to think of both one's returns and costs in terms of what one gets and what one pays after taxes are considered? Wouldn't you also need to adjust both returns/rates with the inflation rate over the time compared? Just to better compare apples to apples? I'm not sure of the answer, just a thought.