Question

Yon made contributions to a Traditional IRA over the course of 35 working years. Her contributions averaged $2,000 annually. Yon was in the 28% tax bracket during her working years. The average annual rate of return on the account was 6%. Upon retirement, Yon stopped working and making IRA contributions. Instead, she started living on withdrawals from the retirement account. At this point, Yon dropped into the 15% tax bracket. Factoring in taxes, what is the effective value of Yon’s Traditional IRA at retirement? Assume annual compounding.

Answer 1

This is an idiotic, stupid pile of smoke and mirrors.

1) The tax bracket during accumulation means nothing. Don't let them fool you with this. Just delete it and forget about it.

2) The tax bracket during payout means a little more, but not much. It really depends on the WAY the funds are paid out. However, since everything is perfectly scalable, we can use it. Very misleading.

3) The average contribution is not as helpful as you might think.
$10000 $0 $0 $0 $0 gives an average of $2,000
$5000 $0 $0 $0 $5000 gives an average of $2,000
$0 $0 $0 $0 $10000 gives an average of $2,000
Are those accumulations even remotely the same? No!! HOW was the money paid in? The average is just not very helpful.

4) The average ROR of 6% has the same sort of problem. Depending on exactly how it was calculated, maybe it's helpful. Hard to say.

How's that? We haven't even started to figure out an answer and we've identified four significant deficiencies!! Wow!!

Assume:
Deposit Timing: End of Each Year
Deposit Amount: Exactly $2,000 each year.
Interest: Exactly 6% each year, paid in arrears, compounded annually.

End of year 1: $2.000
End of year 2: $2.000 + 2000(1.06)
End of year 3: $2.000 + 2000(1.06)
...
End of year 35: $2.000 + 2000(1.06) + ... + 2000(1.06)^34

Can you add those up?
We still haven't done anything about the taxes during the distribution phase.

Answer 2

just to clarify is the 2.000 you wrote meant to be two thousand?

Answer 3

Fair enough. Can you add them up?

Answer 4

So it would be 2120^34?

Answer 5

or ^35?

Answer 6

@jim_thompson5910 @mathslover @mathstudent55

Answer 7

@Hero

Answer 8

You have forgotten your order of Operations.

End of year 35: $2.000 + 2000(1.06) + ... + 2000(1.06)^34
End of year 35: $2.000[1 + 1.06 + 1.06^2 + ... + (1.06)^34]

Can you add those up inside the parentheses?