### Determining your 401(k) Contributions

On January 1, 2006, many companies began to offer the Roth 401(k): an alternative to the traditional 401(k) that allows you to contribute your money in after-tax dollars, rather than pre-tax dollars. Most (in my opinion incorrectly) summarize the difference as the following choice: “*If you think you might be in a higher income tax bracket when you withdraw the funds, invest in the Roth 401(k). Otherwise, invest in a traditional 401(k)*.” Omar Shahine points to a good summary here: http://www.shahine.com/omar/Roth401k.aspx. (This started as a comment on that article, but quickly grew to a post in of itself.)

Here are some examples, for somebody that is married, filing separately.

Current Income | Post-Retirement Income (estimated) | Current Tax Rate (marginal) | Post-Retirement Tax Rate (effective) * | Roth or Traditional | Difference per $1000 |
---|---|---|---|---|---|

30,000 | 30,000 | 15% | 13% | Traditional | 0 |

30,000 | 60,000 | 15% | 19% | Roth | 40 |

30,000 | 90,000 | 15% | 22% | Roth | 70 |

30,000 | 120,000 | 15% | 25% | Roth | 100 |

30,000 | 200,000 | 15% | 28% | Roth | 130 |

60,000 | 30,000 | 25% | 13% | Traditional | 120 |

60,000 | 60,000 | 25% | 19% | Traditional | 60 |

60,000 | 90,000 | 25% | 22% | Traditional | 30 |

60,000 | 120,000 | 25% | 25% | Roth | 0 |

60,000 | 200,000 | 25% | 28% | Roth | 30 |

90,000 | 30,000** | 28% | 13% | Traditional | 150 |

90,000 | 60,000** | 28% | 19% | Traditional | 90 |

90,000 | 90,000 | 28% | 22% | Traditional | 60 |

90,000 | 120,000 | 28% | 25% | Traditional | 30 |

90,000 | 200,000 | 28% | 28% | Roth | 0 |

120,000 | 30,000** | 33% | 13% | Traditional | 200 |

120,000 | 60,000** | 33% | 19% | Traditional | 140 |

120,000 | 90,000** | 33% | 22% | Traditional | 110 |

120,000 | 120,000 | 33% | 25% | Traditional | 80 |

120,000 | 200,000 | 33% | 28% | Traditional | 50 |

200,000 | 30,000** | 35% | 13% | Traditional | 220 |

200,000 | 60,000** | 35% | 19% | Traditional | 160 |

200,000 | 90,000** | 35% | 22% | Traditional | 130 |

200,000 | 120,000 | 35% | 25% | Traditional | 100 |

200,000 | 200,000 | 35% | 28% | Traditional | 70 |

** Assumes that tax rates will be the same as they are today.Higher future tax rates would increasingly favour a Roth 401(k), while lower rates would favour a Traditional 401(k)*

*** Unlikely, given a medium-to-aggressive savings philosophy that would normally guarantee a higher post-retirement income*

Effective tax rates generated by http://www.moneychimp.com/features/tax_brackets.htm

Notice the “Difference per $1000” column. That shows how many dollars (per $1000) it costs if you make a mistake. Worrying about making a mistake causes people a lot of heartburn, so let’s drill into that a bit more. What’s the worst mistake you can make? It’s the row that shows you earning $200,000 now, contributing to a Roth 401(k), and then withdrawing $30,000 per year during retirement. Over your entire 30-year retirement, that would cost 30 years * $30,000 per year / 1,000 * 220 wasted per thousand = $198,000. That’s about $6600 per year. Not good, but not the end of the world. Given a medium-to-aggressive savings strategy, this scenario is also highly unlikely.

How should you estimate your post-retirement income? It will be based on how much you’ve managed to save before retirement, which is a dependent on how much you can save per year. Assuming a 6% annual rate of return, this PowerShell calculation shows how to estimate your “nest egg” for retirement, assuming that you contribute $5,000 per year:

PS >$balance = 0

PS >$contribution = 5000

PS >1..30 | % { $balance += $contribution; $balance *= 1.06 }

PS >$balance

419008.386940671

Now, for your annual retirement income, you can play around with your withdraw rate on this $419,008 nest egg until the final balance nears zero:

PS >$balance = 419008; 1..30 | % { $balance -= 28700; $balance *= 1.06 }; $balance

1460.60834058789

So, contributing around $5,000 per year gives you a post-retirement income of about $29,000. That will remain $29,000 if the contributions were through a Roth 401(k), but will turn to about $25,000 if the contributions were through a traditional 401(k).

Here’s one thing that may play a part in your 401(k) calculations: how much you can hope to retire with. Both the traditional and Roth 401(k) plans have annual contribution limits of $15,500 (expected to increase by $500 per year.) If you are in a position to save the maximum, your choice of 401 vehicle makes a significant difference on your post-retirement income if you base it on your 401(k) alone.

If you manage to save the maximum contribution per year, that leaves you with:

PS >$balance = 0

PS >$contribution = 15000

PS >1..30 | % { $balance += $contribution; $balance *= 1.06; $contribution += 500 }

PS >$balance

1690372.4723898

Which gives an annual retirement income of about $116,000:

PS >$balance = 1690372; 1..30 | % { $balance -= 115800; $balance *= 1.06 }; $balance

4402.41939379471

If those funds were contributed through a traditional 401(k), that will shrink to about $87,000 after taxes. If those funds were contributed through a Roth 401(k), they will stay ay $116,000. Given the tax advantage of the Traditional 401(k), though, it may make sense in that situation to maximize your contribution to the Traditional 401(k), and apply the money you would have invested in the Roth 401(k) to other investment vehicles.

The interest earnings on those other vehicles will be taxed at 10%, though, so the answer to this is highly dependent on your personal situation. Take a salary that seems to most highly favour the Traditional IRA, but where that person can afford to max out the Roth 401(k). That is at the 35% tax bracket:

## Scenario 1: Max out Traditional

### A) First, max out Traditional

```
$balance = 0
$contribution = 15000
1..30 | % { $balance += $contribution; $contribution += 500; $balance *= 1.06 }
$balance
```

(returns 1690372 in total Traditional savings)

```
$balance = 1690372
1..30 | % { $balance -= 115800; $balance *= 1.06 }
$balance
```

(results in $115,800 per year, and tax will be applied)

### B) Then, apply your extra (vs. the Roth) to index funds

```
$balance = 0
$contributed = 0
$marginalTaxRate = 1.35
$limit = 15000
$contribution = (($limit * $marginalTaxRate) - $limit) / $marginalTaxRate
1..30 | % {
$balance += $contribution
$contributed += $contribution
$balance *= 1.06;
$limit += 500
$contribution = (($limit * $marginalTaxRate) - $limit) / $marginalTaxRate
}
$balance = ($balance - $contributed) * 0.9 + $contributed
$balance
```

(results in 411725.799113175 in total additional index fund savings, after taxes )

```
$balance = 411725
1..30 | % { $balance -= 36200; $balance *= 1.06 }
$balance
```

(results in 28,200 per year (after taxes))

### C) Then figure out the combination of investments

Total = 144,000 pre tax (A + B) at 25% effective tax rate = 115,050 per year after tax (0.75 * A + B)

## Scenario 2: Max out Roth

```
$balance = 0
$contribution = 15000
1..30 | % { $balance += $contribution; $balance *= 1.06; $contribution += 500 }
$balance
```

(results in 1690372.4723898 total savings)

```
$balance = 1690372
1..30 | % { $balance -= 115800; $balance *= 1.06 }
$balance
```

(results in 115,800 per year tax free)

Lower tax brackets than 35% (ie all of them) favour the Roth even more heavily if that person can afford to max out their contributions. As always, make your own informed decisions regarding investments, but hopefully this exercise can help clarify some things.

*[Edit: Updated table – Brian Kramp reminded me that Roth 401(k) contributions are taxed at your marginal tax rate, not the effective tax rate.][Edit2: Added calculations for investing in index funds]*