The Situation: Consider a person who took out a 30-year mortgage, 15 years prior to retirement. The initial balance on the mortgage was $600,000 and the interest rate on the mortgage was 3.6 percent.
The person retires with $1,000,000 in her 401(k) plan but the retiree also has an outstanding mortgage of $378,975 and an ongoing monthly mortgage payment of $2,728.
The retiree plans to spend $40,000 per year $3,333 per month to cover non-housing consumption in retirement.
- The total annual disbursement from a 401(k) plan for a person with a mortgage is $72,735.
- The total annual disbursement from a 401(k) plan for a person without a mortgage is $40,000.
Question One: What are the outstanding balances of the retirement plan after 15 years for a person with a mortgage and a person without a mortgage if the rate of return on investments in the retirement plan is 6.0 percent per year?
Answer:
- The outstanding 401(k) balance after 15 years for the person with a mortgage is $691,380.
- The outstanding 401(k) balance after 15 years for the person without a mortgage is $1,484,698.
Question Two: What are the 401(k) outstanding balances after 15 years if the person started retirement with $900,000 in 401(k) assets.
Answer:
- The person with the mortgage has a 401(k) balance of $445,971 after 15 years.
- The person without a mortgage has a 401(k) balance of $1,239,290 after 15 years.
Implications for longevity risk:
The existence of a mortgage payment substantially increases the depletion rate of the 401(k) plan. The mortgage payment cannot be avoided during market fluctuations. The existence of a mortgage during a market downturn at the beginning of retirement can have an especially adverse impact on retirement wealth.
The discussion presented here does not explicitly consider taxes.
- All traditional 401(k) assets are fully taxed as ordinary income.
- The person with higher spending due to a mortgage will have also have higher taxes.
- This person may increase spending to have adequate non-housing consumption.
More on these issues will follow.
Technical Note: Discussion of Financial Calculations
The most straight forward way to obtain the 401(k) balance is to set up a spreadsheet where the loan payment is subtracted from the balance each month and the balance minus the loan payment earns a monthly return.
A second approach involves the use of the FV function.
The arguments of the FV function are
- Rate 0.06/12 or 0.005.
- NPER 12*15 or 180.
- PMT 6061.21 for person with a mortgage and $3,333.33 for person without the mortgage.
- PV -1,000,000. Negative because PV is cash in and must be the opposite sign of the PMT function.
The FV function is set up to analyze loans, so be careful with the sign of answer.