How long will my money last in retirement

Scicaster

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Hello,
I'm 65 years old and about to retire. I have $875,000 in my $401k account. I want to withdraw $5,000 per month going forward. The $875,000 is all pre-tax money so whenever I make a withdrawal I'll have to pay 17.5% in taxes. Assuming the money that remains in the account earns 5% annual rate of return how many months before my money runs out?
Thanks
 

tkhunny

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1) It's all pre-tax, so we can just ignore the taxation. You'll just have to get used to receiving $5,000.00, but being able to use only $4,125.00

2) You must solve this equation for "n".

Some necessary calculations:
i = 0.05
r = (1+i)^(1/12) = 1.0040741238
v = 1/r = 0.9959424074

Here's the equation:
875000 = 5000(v + v^2 + v^3 + ... + v^n)

Some Division

175 = v + v^2 + v^3 + ... + v^n

You could just guess at this and you would have to solution in just a bot of time, but there is a better way. I'll just throw it out there, for free.

175 = v + v^2 + v^3 + ... + v^n = \(\displaystyle \dfrac{v - v^{n+1}}{1-v}\)

After that, it's just arithmetic (if you count logarithms as arithmetic).

0.7100787136 = \(\displaystyle v - v^{n+1}\)

0.7129716622 = \(\displaystyle 1 - v^{n}\)

\(\displaystyle v^{n}\) = 1 - 0.7129716622 = 0.2870283378

n log(v) = log(0.2870283378)

n = log(0.2870283378)/log(v) = 306.9899889945 -- Right close to 307 months. (A little over 25½ years.)

If you have a long family history of living well past 90 years of age, you may wish to consider a life-contingent option.
 

Scicaster

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WOW! Thanks so much. This will help us a lot with our retirement planning.
 

Dr.Peterson

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In case it matters, I put this into Excel and got 311.48 months (almost 6 full years). I may have entered something wrong, or it may be assuming a different kind of interest. But at least if tkhunny is wrong, it's on the side of caution.
 

Subhotosh Khan

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In case it matters, I put this into Excel and got 311.48 months (almost 6 full years). I may have entered something wrong, or it may be assuming a different kind of interest. But at least if tkhunny is wrong, it's on the side of caution.
You meant 26 full years - right?
 

Dr.Peterson

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The 2 key must not have been working. I know I hit it.
 

tkhunny

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In case it matters, I put this into Excel and got 311.48 months (almost 6 full years). I may have entered something wrong, or it may be assuming a different kind of interest. But at least if tkhunny is wrong, it's on the side of caution.
5% Effective, Payments at the end of the month: 306.99 months <== TKHunny
5% Nominal, Compounded monthly to yield 5.116%, Payments at the end of the month: 314.15
5% Effective, Payments at the beginning of the month: 304.52 months
5% Nominal, Compounded monthly to yield 5.116%, Payments at the beginning of the month: 311.48 <== Dr.Peterson

It's a matter of how interest is actually credited and when payments actually are made.

Fortunately, for retirement planning, "Somewhere in the neighborhood of 25 years" is often close enough. :)
 
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JeffM

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I hate to disagree with tkhunny, but the returns may not grow tax free due to required minimum distributions. At some point you may have to start withdrawing more than the 60,000 annually that you are planning on. That excess cannot be invested tax free. Furthermore, you need to think about inflation risk. 60,000 annually plus social security may be adequate for now, but will it be adequate ten years from now. Moreover, at current market rates, earning 5% annually will require incurring market risk. Finally, if you are married, you need to think about not just one person's longevity, but two, and the change in required income for one rather than two.

I have not found most financial planners to be very sophisticated, but retirement planning is not something to do lightly without some level of professional help.
 

tkhunny

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No disagreement at all. Excellent points:
  • RMD's are adequately substituted by Systematic Life-Contingent Withdrawals. More on this, later.
  • In this particular example, the RMD peaks at just under $49,400 at age 78. $5,000 / month will be fine throughout the process.
  • Inflation risk is real, but Cost of Living increases are very expensive. It's a difficult trade-off.
  • An additional life is a tricky business. A reliable company providing a Joint-and-Survivor Annuity can help with that, but again, it costs. And don't fall for the fallacy that one person needs HALF of what two people need. ½ is not a good number for that. There are fixed costs, not just marginal costs.
  • Beneficiaries are also important. DO NOT buy a Life-Only annuity. If you die tomorrow, neither you nor your descendants get ANYTHING. Life-Contingent annuities MUST have at lease SOME guarantees IMHO.
  • Changes in Tax Laws are also very real. It is gloriously difficult to predict what this might do.
  • If you have a 5% permanent guarantee on these funds, hold on tight. Don't let that go!
Well, that's enough team retirement planning for one day. :)
 

Scicaster

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Thank you all so much. A little more background, my wife (laid off due to Covid) and I plan to retire Feb 1, 2021. I figure we should receive about $4000 per month from Social Security and qualify for Medicare. Of course unexpected financial costs will have an impact, but I want to at least have a game plan. Thanks again,
Regards,
Scicaster
 

davidshoff

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Apr 2, 2021
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1) It's all pre-tax, so we can just ignore the taxation. You'll just have to get used to receiving $5,000.00, but being able to use only $4,125.00

2) You must solve this equation for "n".

Some necessary calculations:
i = 0.05
r = (1+i)^(1/12) = 1.0040741238
v = 1/r = 0.9959424074

Here's the equation:
875000 = 5000(v + v^2 + v^3 + ... + v^n)

Some Division

175 = v + v^2 + v^3 + ... + v^n

You could just guess at this and you would have to solution in just a bot of time, but there is a better way. I'll just throw it out there, for free.

175 = v + v^2 + v^3 + ... + v^n = \(\displaystyle \dfrac{v - v^{n+1}}{1-v}\)

After that, it's just arithmetic (if you count logarithms as arithmetic).

0.7100787136 = \(\displaystyle v - v^{n+1}\)

0.7129716622 = \(\displaystyle 1 - v^{n}\)

\(\displaystyle v^{n}\) = 1 - 0.7129716622 = 0.2870283378

n log(v) = log(0.2870283378)

n = log(0.2870283378)/log(v) = 306.9899889945 -- Right close to 307 months. (A little over 25½ years.)

If you have a long family history of living well past 90 years of age, you may wish to consider a life-contingent option.
5% Effective, Payments at the end of the month: 306.99 months <== TKHunny
5% Nominal, Compounded monthly to yield 5.116%, Payments at the end of the month: 314.15
5% Effective, Payments at the beginning of the month: 304.52 months
5% Nominal, Compounded monthly to yield 5.116%, Payments at the beginning of the month: 311.48 <== Dr.Peterson

It's a matter of how interest is actually credited and when payments actually are made.

Fortunately, for retirement planning, "Somewhere in the neighborhood of 25 years" is often close enough. :)
Hi tkhunny
It took a long time to understand this calculation but I got some idea from your explanation. Now I can manage mysuper in the correct way. It helps me a lot. Also, I found a relevant article about how we can manage our funds after retirement........ commercial URL deleted
 
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