## Wednesday, December 4, 2013

### Mortgage payments versus 401(k) contributions by older workers

Should older workers accelerate payments of their mortgage?

The situation:   A 45 year-old man took out a \$500,000 30-year mortgage.  The interest rate on the loan was 6.0%  The person is now 55 years old and considering whether to pay off the mortgage quickly or continue to make the maximum payment to his 401(k) plan.

This post discusses the impact of his choice between adding money to his 401(k) versus paying off his mortgage on his future financial prospects and his ability to maintain his current residence during retirement.

Questions on this situation:

What is the monthly payment on the mortgage?

What is the balance on the mortgage at age 55?

What will the balance on the mortgage be at age 65 based on the current scheduled payment?

What monthly payment would result in a \$0 mortgage balance at age 65?

Arithmetic Calculations:

What is the monthly payment on the mortgage?

Put r=0.005, per=360, PV=\$500,000 and FV-\$0 in the PMT function.  The monthly mortgage payment is \$2,997.75. The yearly payment on the mortgage is \$34,973.03.

What is the balance on the mortgage at age 55?

Put r=0.005, per=120, pmt=\$2997.75, and PV=\$500,000 in the FV function and get the future value of the loan 10 years after it is issued.  The loan balance after 10 year is \$418,428.62.

What will the balance on the mortgage be at age 65 based on the current scheduled payment?

Put r=0.005, per-240, PMT=\$2997.75 and PV=\$500,000 in the FV function.  The loan balance after 20 years of payments is \$270,018.

What monthly payment would result in a \$0 mortgage balance at age 65?

This requires calculation of the payment on a 10-year 6.0% loan with an initial value equal to the current balance which is \$418,428.62.  Use the PMT function (r=0.005, PER=120, PV=\$4187,429, and FV=0)  We get \$4645.42.

Confirm the answer is correct by placing the \$4,645.42 payment estimate into a FV function for a 10 year loan when the initial value is \$418,429 and r=0.005.  Happily I get FV=\$0.

Financial Assessment: Most financial advisors would recommend that this retiree contribute the maximum allowable amount to his 401(k) in his last 10 working years and continue to pay the minimum on his mortgage.  This example illustrates the limitations (I would argue folly) of this advice.

If the person in this example continues to pay the minimum on his mortgage he will still have \$270,000 in mortgage debt at age 65.

He could continue making his mortgage payment until age 75.  This amounts to \$349,070 over 10 years with \$79,052 of the payments in interest.  The retiree would have to pay additional tax If the source of payments is 401(k) disbursements.  Assuming a marginal tax rate of 0.20 total additional disbursements needed to cover both taxes and mortgage payments would be around \$436,000.

The retiree could pay off the entire loan at age 65.   This person would likely have a marginal tax rate of 35% if he chooses to make a lump sum payment.  The total 401(k) disbursement needed to pay off the mortgage and taxes is around  \$415,000.

I used the rate function in my numbers spreadsheet to find the rate of return needed to turn \$1,648 monthly payments into \$415,000 in 10 years.  My answer was over 13.0%.  Even if you retire in a boom year you may not have enough to pay off the mortgage.

More importantly, there is risk to holding stock.  By contrast, debt payments are certain unless you are willing to default.

In my view, the conventional wisdom that one should keep a large mortgage and build their 401(k) plan is just plain wrong.  Paying off the mortgage needs to be the highest priority of older workers, especially if they are planning to stay in their current home during retirement.