Question

Suppose that Ramos contributes $6000/year into a traditional IRA earning interest at the rate of 4%/year compounded annually, every year after age 35 until his retirement at age 65. At the same time, his wife Vanessa deposits $4700/year into a Roth IRA earning interest at the same rate as that of Ramos and also for a period of 30 years. Suppose that the investments of both Ramos and Vanessa are in a marginal tax bracket of 25% at the time of their retirement and that they both wish to withdraw all of the money in their IRAs at that time.

(a) After all due taxes are paid, who will have the larger amount?

Answer 1

Calculation of Amount of withdrawl after all taxes at the time of retirement:

Particulars	Ramos	Vanessa
Deposit per year	6000	4700
Interest Rate P.a	4%	4%
Compounded	Annually	Annually
Period	30 years	30 years
Future Value	C*[(1+i(1-t))^n-1/i*(1-t)]
C              =	Cash flow per period
i              =	Interest Rate
n                =	Number of Payments
t                 =	Tax
Future Value    =	6000[((1+(0.04*0.75))^30-1/0.04*0.75]	4700[(1.04*0.75)^30-1/0.04*0.75]
=	6000[(2.43-1)/0.03]	4700[(2.43-1)/0.03]
=	6000[(1.43)/0.03]	4700[(1.43)/0.03]
Future Value of Investments after Tax	$                                              2,86,000.00	$                                      2,24,033.33

Therefore, as per above after all the dues paid Ramos will have the larger amount.