Kirby made contributions to a Roth IRA over the course of 35 working years. His contributions averaged $2,000 annually. Kirby was in the 26% tax bracket during his working years. The average annual rate of return on the account was 5%. Upon retirement, Kirby stopped working and making Roth IRA contributions. Instead, he started living on withdrawals from the retirement account. At this point, Kirby dropped into the 15% tax bracket. Factoring in taxes, what is the effective value of Kirby’s Roth IRA at retirement? Assume annual compounding.
$170,140.61
$172,940.61
$162,440.61
$133,674.0

Question

Kirby made contributions to a Roth IRA over the course of 35 working years. His contributions averaged $2,000 annually. Kirby was in the 26% tax bracket during his working years. The average annual rate of return on the account was 5%. Upon retirement, Kirby stopped working and making Roth IRA contributions. Instead, he started living on withdrawals from the retirement account. At this point, Kirby dropped into the 15% tax bracket. Factoring in taxes, what is the effective value of Kirby’s Roth IRA at retirement? Assume annual compounding.
 $170,140.61
 $172,940.61
 $162,440.61
 $133,674.0

anonymous · Answer

Do you know if those contributions are taxed?

anonymous · Answer

P(1.05^35 +1.05^34 + 1.05^33 + 1.05^32... + 1.05^2 + 1.05)
This seems to be the simplest I can get it, which still requires some really tedious calculation...
And I could explain to you how I got that, if you like.

anonymous · Answer

Oh, and P would be the annual amount added to the account. Either 2000 or 1480, depending on whether or not it is taxed.

anonymous · Answer

Oh, and that would be really a pain to calculate. Luckily Wolfram Alpha is a freaking boss and does summations =) http://www.wolframalpha.com/input/?i=summation&a=*C.summation-_*Calculator.dflt-&f2=1.05%5En&f=Sum.sumfunction_1.05%5En&f3=1&f=Sum.sumlowerlimit_1&f4=35&f=Sum.sumupperlimit_35&a=*FVarOpt.1-_**-.***Sum.sumvariable---.*--