Question

Suppose that Ramos contributes $5500/year into a traditional IRA earning interest at the rate of 5%/year compounded annually, every year after age 37 until his retirement at age 67. At the same time, his wife Vanessa deposits $3850/year (the amount after paying taxes at the rate of 30%) into a Roth IRA earning interest at the same rate as that of Ramos. Suppose that Ramos withdraws his investment upon retirement at age 67 and that his investment is then taxed at 30%. (Round your answers to the nearest cent.)

(a)How much will Ramos's investment be worth (after taxes) at that time?

(b)How much will Vanessa's investment be worth at that time?

Answer 1

		Ramos Savings:
	Rate	Interest rate	5%
	Nper	Number of years	30	(67-37)
	Pmt	Amount of deposit per year	$5,500
	FV	Future value of savings at age 67	$365,413.66	(using FV function of excelwith Rate=5%,Nper=30, Pmt=-5500)
		Excel Command: FV(5%,30,-5500)
		Taxes on savings=30%*365413.66=	$109,624.10
		Ramos Savings after taxes	$255,789.56	(365413.66-109624.10)
		Vanessa Savings:
	Rate	Interest rate	5%
	Nper	Number of years	30	(67-37)
	Pmt	Amount of deposit per year	$3,850
	FV	Future value of savings at age 67	$255,789.56	(using FV function of excelwith Rate=5%,Nper=30, Pmt=-3850)
		Excel Command: FV(5%,30,-3850)
		Vanessa Savings	$255,789.56
		This can also be calculated by using Factor
		Compound Amount Factor=CAF
		CAF=(F/A,i,N)=(((1+i)^N)-1)/i
		i=interest rate=0.05
		N=number of years=30
		CAF=(F/A,5%,30)=((1.05^30)-1)/0.05	66.4388475
		Ramos savings(Before taxes)=CAF*5500=	$365,413.66
		Ramos savings(After taxes)=(1-0.3)*365413.66	$255,789.56
		Vanessa Savings =CAF*3850=	$255,789.56