Kobe made contributions to a Roth IRA over the course of 25 working years. His contributions averaged $5,000 annually. Kobe was in the 27% tax bracket during his working years. The average annual rate of return on the account was 4%. Upon retirement, Kobe stopped working and making Roth IRA contributions. Instead, he started living on withdrawals from the retirement account. At this point, Kobe dropped into the 15% tax bracket. Factoring in taxes, what is the effective value of Kobe’s Roth IRA at retirement? Assume annual compounding.

please help, ive tried but cannot seem to get an answe

Question

Kobe made contributions to a Roth IRA over the course of 25 working years. His contributions averaged $5,000 annually. Kobe was in the 27% tax bracket during his working years. The average annual rate of return on the account was 4%. Upon retirement, Kobe stopped working and making Roth IRA contributions. Instead, he started living on withdrawals from the retirement account. At this point, Kobe dropped into the 15% tax bracket. Factoring in taxes, what is the effective value of Kobe’s Roth IRA at retirement? Assume annual compounding. 

please help, ive tried but cannot seem to get an answe

anonymous · Answer

answer choices:
$189,479.54

$152,007.56

$193,229.54

$174,479.54

tkhunny · Answer

We have 4% earnings.

Are the earning in a ROTH Taxable?

If so, use (4%)*(1 - 0.27) as the earnings rate in order to include the effect of taxes.

If not, use 4% during the accumulation phase and just ignore the taxes.

In either case, define r = (1 + Earnings Rate) to be an annual accumulation factor.

When are payments made?

The END of each year?  Use $5000\dfrac{1 - r^{25}}{1-r}$ for the total accumulation before consideration of taxes after retirement.

The BEGINNING of each year?  Use $5000\dfrac{r - r^{26}}{1-r}$ for the total accumulation before consideration of taxes after retirement.

How shall we treat retirement taxes?

Consider then due immediately, find 85% of the value.
Ignore them, since they are not yet paid?  Us the value and ignore the taxes.

This results in the following possibilities.

NonTaxable, Beginning, Ignore $216,558
NonTaxable, Beginning, Pay $184,074
NonTaxable, End, Ignore $208,229
NonTaxable, End, Pay $176,995
Taxable, Beginning, Ignore $185,661
Taxable, Beginning, Pay $157,811
Taxable, End, Ignore $180,393
Taxable, End, Pay $153,334

$189,479.54 - Don't see it.
$152,007.56 - Don't see it.
$193,229.54 - Don't see it.
$174,479.54 - Don't see it.

Well, then!  Where does that leave us?

You will have to demonstrate the methods of your classroom instruction or text book or online lectures.  Show your work!