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Your Mortgage May Not Be As Expensive As You Think It Is
By JLP | August 27, 2007
UPDATE: I updated the formula due to an error on my part that was caught by Brad of Analyzing Wealth. Thanks for the catch, Brad!
Did you know that your mortgage may not be as expensive as you think it is? It’s true. If you have a mortgage with a fixed interest rate, which holds your payment constant, your mortgage is cheaper than you think it is.
Why?
Inflation.
For example…
Say you take out a 30-year $200,000 mortgage at a fixed rate of 6.5%. Your monthly payment would be $1,264.14. Your total payments over the life of this mortgage would be $455,089 of which $255,089 would go to pay interest. However, that’s not entirely accurate because we aren’t factoring in inflation.
Normally when we talk about inflation, we talk about the gradual decrease in the purchasing power of a dollar. Although inflation works to our disadvantage when it comes to purchasing power, the opposite is true when it comes to paying off a mortgage (or pretty much any type of loan).
If inflation averages 3% per year, in 10 years, the $1,264.14 payment would have about $941 in purchasing power. In other words, had the mortgage payment increased with the inflation rate, the payment would be nearly $1,700 per month. However, the mortgage payment is still just $1,264.14.
I put together a spreadsheet to calculate the inflation-adjusted cost of the mortgage used in this example. To make the calculation I simply discounted each payment by the periodic inflation rate, which was .2466%. Then I summed all the discounted payments to arrive at the inflation-adjusted cost of the mortgage. The formula for discounting a payment (also called a cashflow) looks like this:
where:
Payment = $1,264.14
i = inflation rate of 3% or .03 raised to 1/12 since there are 12 payments per year
n = number of the payment
So, the first discounted cashflow looks like this:
This calculation is really easy to perform with the aid of a spreadsheet. Anyway, I came up with an inflation-adjusted total cost of $301,398 for this mortgage compared to $455,089 before the inflation adjustment.
The bottom line: mortgages aren’t as expensive as we think they are after we figure in the effects of inflation. This is especially important to think about when trying to decide between renting or buying. What are the chances of not facing a rent increase over 30 years?
Related:
Topics: Financial Math Basics, Housing Market, Mortgages | 14 Comments »
August 28th, 2007 at 8:28 am
You highlight one of the great reasons home ownership is generally a positive factor in wealth creation!
August 28th, 2007 at 8:32 am
A minor quibble: shouldn’t the periodic rate of inflation be 0.2466%, not 0.25%? I know you are using a standard formula but I believe that formula is not precise. If you use the arithmetic mean you overstate annual inflation– 1.0025^12=1.03042. You need to spread the rate out over 12 months geometrically– 1.03^(1/12)– not arithmetically as the formula does. There’s not much difference (only $6 in the 360th month) but I wanted to throw this out there as I think this commonly used formula is slightly flawed, and in other applications it could throw someone off considerably.
However, this is a really good point to make. As rent goes up, mortgages stay constant. The longer you stay, the less you pay (relatively) for your housing. Another argument for owning over renting– you lock in a payment.
August 28th, 2007 at 9:08 am
Brad,
Yes, you are correct. I was using Excel with the cells formatted to percentage rounded two places past the decimal. So, when I divided 3% by 12, I got .25%, which was rounded. I’ll make the changes.
Thanks for being so alert.
August 28th, 2007 at 9:36 am
Sorry to get nitpicky. I just had a major argument with a coworker over the use of arithmetic and geometric means to show periodic returns, so it’s fresh on my brain.
I’m going to have to think on this subject for awhile. When considered as a leveraged investment, the early part of a mortgage is most profitable (or disastrous if the value goes down), and the longer you own the home, the lower your returns will be (due to decreased leverage). But I never factored inflation into that equation, and that actually helps a home, as an investment, remain more profitable over renting for a longer period of time. Good stuff, JLP.
August 28th, 2007 at 11:13 am
JLP/Brad, It’s been awhile since high school algebra, could you explain in layman’s terms the difference between the geometric and arithmatic means and when you would use one over the other. Thanks
Also, this thread very much highlights the potential of rental property in building wealth. In general, rents increase with inflation making for a stable, inflation-adjusted income stream, while the inflation-adjusted value of fixed loan payments decreases over time. It’s a beautiful combination. Also, tax treatment of rents can be quite favorable.
I live next to a number of “Millionaire Next Door” types – regular people (teacher, nurse, govt types, etc.) who bought up multiple rental buildings in our neighborhood in their younger days, now live off the rental income, and are 8-digit millionaires on paper (not that I’m pushing the whole RK thing). They never imagined the kinds of rents they can now charge these days. And I get the feeling the capital appreciation is just a bonus they don’t even pay much attention to.
August 28th, 2007 at 11:37 am
Miguel,
Sure, read this post:
Average vs. Geometric Average
August 28th, 2007 at 12:48 pm
Excellent… thanks.
So, if I understand correctly, sounds like “geometric mean” in this context is the same as “compound annual growth rate”.
August 28th, 2007 at 12:50 pm
Miguel said:
So, if I understand correctly, sounds like “geometric mean” in this context is the same as “compound annual growth rate”.
Yes, that’s correct.
August 28th, 2007 at 3:21 pm
I hadn’t thought of it that way, but it still doesn’t change the fact that I am going to try to pay the mortgage off early and then not have a monthly payment at all.
August 28th, 2007 at 3:23 pm
Blaine,
BEFORE you do that, please read through all the posts I have put together on mortgages.
August 28th, 2007 at 6:19 pm
Nice job! I feel so much better about the 28.5 years remaining on my mortgage!
August 28th, 2007 at 11:34 pm
The point you are making, JLP, is that one should _never_ sum a payment stream without first discounting all payments to their present value. The fact that a mortgage’s payments sum to $455,089 is totally irrelevant.
August 29th, 2007 at 11:04 am
Thanks for the detailed analysis. Where can I access the spreadsheet?
October 6th, 2007 at 9:17 am
[...] Excellent point on taking on a mortgage that I hadn’t thought on before. Factoring in inflation and your mortgage payment. [...]