Could the title of this post be any longer?

Matt in Manhattan sent this question via email.  I thought I'd share the conversation because it makes for good learning. 

The question (edited for length and clarity):

The payment on a 30-year fixed mortgage for $1,000,000 is $6,418.  The same payment on a 5-year ARM with the interest only option is $5,428, or about $1,000 less per month.

Other than the risk that my ARM will adjust higher in the future, is anything lost by taking the 5-year ARM with interest only and paying an extra $1,000 every month to reduce principal?

In which scenario will I have more equity in 5 years?

This is a terrific question with many angles to it.  For purposes of answering the question, though, I want to focus on the math. 

Focusing on math forces me to ignore basic mortgage planning concepts that would preclude me from ever having this conversation with a client.  But, because Matt asked, I am sure that other readers are interested in the actual answer to the question, too.

For Kurt, Brian, Russell and others that will comment about the plan being foolish to begin with, please consider the following bullet points my own personal disclaimer.  This is a purely mathematical discussion and is irrelevant with respect to sound financial planning because I am unilaterally believe:

• Interest only loans increase cash flow for safe investments; home equity is not a safe investment.
• Home equity does not earn a rate of return.
• Dollars placed in a safe, liquid account will earn compounded interest over time and, therefore, have higher utility than dollars used to pay down a mortgage.

Disclaimers done.

Now, I especially like this question because the reader lives in Manhattan where properties are super expensive versus the rest of the nation.  Matt's figures are nice, large numbers and that helps to exaggerate our conclusions.  I like that.

Oh, and how expensive is "super expensive"?  Try $950 per square foot.  Noah can tell you all about it. 

Back to the question.  Matt asked, "Which plan creates more equity?"  The answer is that it's a tie.  Both plans create exactly zero dollars worth of equity.  How can that be?  Because there are two ways to increase the amount of equity in a home.

1. Pay down the principal balance on the mortgage.  This increases the difference between what is owed on the home and what the home is worth.
2. Let the home's value increase over time.  This increases the difference between what is owed on the home and what the home is worth.

Both methods increase home equity positions and, because of that, homeowners often confuse and mischaracterize the two. Let's delve deeper.

In Method #1, the homeowner takes dollars from a paycheck that have already been taxed and places them "on deposit" with the home.

In Method #2, the home itself creates value when the market appreciates.

The differences are subtle, but important. 

Method #1 depletes the homeowner's personal funds to "create" equity in a zero sum game -- the gain in equity is 100% offset by a loss in savings.  Method #2, by contrast, creates equity using no personal funds at all.

As the Manhattan condo market appreciates, Matt will gain equity because his home will be worth more on the open market (he hopes!).  Any dollars that he puts towards his mortgage, though, will come from his bank account. 

In that sense, Matt is playing a shell game with his own money, taking funds from one account (the bank) and placing them into another (the home).  The main difference here is that Matt can use an ATM and withdraw his money any time he wants; he can only get the money out from his home if he uses a remortgage, or if he sells.  ATM fees are much lower than remortgage fees.

Oops.  I am hitting my bullet points again about why I would never recommend this strategy.  Back to the math part of the question.  Sorry. 

According to Matt, he has two offers:

• The 30-year fixed mortgage is 6.625% for a payment of $6,403
• The 5-year ARM interest only is 6.500% for a payment of $5,417

Comparing the two plans, Matt's savings in Month 1 is $986.  He wants to invest that into his mortgage to reduce his loan balance.  Because the mortgage has an interest only feature, an interesting thing will happen. 

In Month 2, Matt's mortgage will drop by $5 to $5,411. 

The payment drops because interest only loans only require that interest to be paid on the existing loan balance. 

As the loan balance decreases (Step 1), therefore, so does the monthly payment (Step 2).

Step 1: $1,000,000 - $986 = $999,014
Step 2: $999,014 * 0.065 annual rate / 12 months = $5,411.32

In order to adjust for the change, Matt must increase his principal paydown in Month 2 to $991 from $986.

In Month 3, Matt must increase his paydown again by $5 to $996.  This pattern continues each month until the 60th month when we see that Matt is now investing an extra $1,355 monthly into his mortgage. 

The spreadsheet shows that after five years, Matt will have paid the exact same amount to his mortgage servicer regardless of which plan he followed -- $384,186.58.

However, if Matt had used the 30-year fixed mortgage, his remaining loan balance after 5 years would be $937,445 (and that's not shown above).  Using the 5-year ARM with interest only and "invest the difference", Matt's loan balance is $930,284. 

Choosing the 5-year ARM with interest only saves Matt $7,161 so clearly this is the winning play mathematically.

We should have known this from the start, though, right?  The 5-year ARM carries an interest rate that is 0.125% lower than the 30-year fixed mortgage so -- all things equal -- we should expect a lower carrying cost over 5 years.  Not surprisingly, the $7,161 represents the exact amount of additional interest from taking the 0.125 percent higher rate.

Our conclusion, therefore, is that there is no mathematical benefit to choosing an amortizing loan versus an interest only program and applying the difference toward principal.  The lowest cost option will be the one with the lowest interest rate.

Thanks, Matt, for the great discussion.

Dan Green is an active loan officer. Email or call 513-443-2020. Dan is on Twitter at @mortgagereports.