Question

One of the simplest tax avoidance strategies is to contribute to a Roth IRA, although this may not be right for everyone. Some individuals, particularly low-income households that may be eligible for tax credits because of young children in the home, may benefit more from contributions to a traditional IRA. Here, you want to help Jennifer identify the best retirement savings option for her situation. Jennifer is 25, single, and makes $38,000 a year. Jennifer does not have access to an employer-sponsored retirement plan, but she really wants to start saving for retirement. She can contribute $5,300 of pretax money to a traditional IRA, or she can contribute $4,505 of after-tax money to a Roth IRA. The $795 difference represents the tax that Jennifer has to pay. Assume Jennifer continues to make this same annual contribution for 30 years and earns 9% on her investment.

Answer 1

Given,

Number of investments=30 and rate of interest=9%

Future Value of both options are calculated as that of ordinary annuity, as follows:

Traditional IRA:

Future Value=$722,430. Calculation as follows:

D A B C 1 Future Value of Annuity Payments at the end of each period 2 8 3 Future value of annuity is calculated using the formula FVA=P*{[(1+r)^n]-1/r] 4. Where P= Periodical payments, 5 n= Number of payments. Eg. if number of years=N, then n=N*2 for semi annual payments 6 r= Rate of interest per period in decimals All amounts in $ Given that 9 Periodical payments (P)= 5300 No. of years (N)= 10 Rate of interest (% p.a)= R= 9 No. of payments a year (t)= 11 12 Calculations: 13 Formula Cell reference Value 14 Interest rate per period in decimals (r )= R/(100*t) D10/(100*G10) 0.09 15 No. of periods (n)= N*t G9*G10 16 (1+r)= 1+G14 1.09 (1+r)^n= G164G15 13.2676785 18 [(1+r)^n]-1= G17-1 12.2676785 [(1+r)^n)-1/r= G18/614 136.307539 20 Future value of annuity FVA= P*{[(1+r)^n]-1/r} D9*G19 722429.954 Rounded to $722,430 30 17 19 21

Roth IRA:

Future Value= $614,065. Calculation as follows:

D G A B C 1 Future Value of Annuity E F Payments at the end of each period 2 3 Future value of annuity is calculated using the formula FVA= P*{[(1+r)^n]-1/r] 4 Where P= Periodical payments, 5 n= Number of payments. Eg. if number of years=N, then n=N*2 for semi annual payments 6 r= Rate of interest per period in decimals 7 All amounts in $ 8 Given that 9 Periodical payments (P)= 4505 No. of years (N)= 30 10 Rate of interest (% p.a)= R= 9No. of payments a year (t)= 1 11 12 Calculations: 13 Formula Cell reference Value 14 Interest rate per period in decimals (r )= R/(100*t) D10/(100*G10) 0.09 15 No. of periods (n)= N*t G9*G10 16 (1+r)= 1+G14 1.09 17 (1+r)^n= G164G15 13.2676785 18 [(1+r)^n)-1= G17-1 12.2676785 19 [(1+r)^n]-1/r= G18/G14 136.307539 20 Future value of annuity FVA= P*{[(1+r)^n)-1/r} D9*619 614065.461 21 Rounded to | $614,065 30

Tax rate of Traditional IRA=24%.

Tax amount of traditional IRA= Future value*Tax rate = $722,430*24% = $173,383

Roth IRA: No tax

After tax wealth of Traditional IRA= Future value- Tax amount = $722,430-$173,383 = $549,047

After tax wealth of Roth IRA= Future value of investment stream= $614,065

Since after tax wealth is higher in Roth IRA, the same is better for Jennifer.