Question

Suppose that Ramos contributes $5500/year into a traditional IRA earning interest at the rate of 3%/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%

A) How much will Ramo'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 after taxes $9344.96

Vanessa Savings $9344.96

Explanation:

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 excel with Rate=3%,Nper=30, Pmt=-5500)

Excel Command: FV(3%,30,-5500)

Taxes on savings=30%*365413.66= $109,624.10

Ramos Savings after taxes $9344.96

Vanessa Savings:

Rate Interest rate 3%

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 excel with Rate=3%,Nper=30, Pmt=-3850)

Excel Command: FV(3%,30,-3850)

Vanessa Savings $9344.96

Answer 2

(a)$9344.96

(b)$9344.96

Explanation:

(a)Ramos Contributes $5500/year

Therefore his principal =$5500

Rate, r=3%

Time = 67-37 =30 years

Since it is compounded annually, Period =1

`Ramos\:Amount \: at \: Compound \: Interest\: before\:tax= P(1+r)^n`

`= 5500(1+0.03)^(30)\\=5500(1.03)^30\\=\$13349.94`

Ramos Tax at 30% = 30% of 13349.94 =$4004.98

• Therefore: Worth of Ramos Investment =13349.94 - 4004.98=$9344.96

(b)Vanessa Contributes $3850/year

Therefore her principal =$3850

Rate, r=3%

Time = 67-37 =30 years

Since it is compounded annually, Period =1

`Vanessa\:Amount \: at \: Compound \: Interest= P(1+r)^n`

`= 3850(1+0.03)^(30)\\=3850(1.03)^30\\=\$9344.96`