An individual is considering contributing $ 4,000 per year to either a tradition
ID: 2741627 • Letter: A
Question
An individual is considering contributing $ 4,000 per year to either a traditional or a Roth IRA. Payments would begin in one year. If she uses the traditional IRA, her contributions would be fully deductible. She is 40 years old and is in a 28% tax bracket. On either IRA she can earn 7%. When she retires at age 65 she believes she will be in a 28% tax bracket. Which type of IRA should she choose if she invests not only the $ 4,000 per year, but any tax savings due to the deductibility of her contributions in a taxable investment earning a pretax rate of 7% ? She will withdraw all her money upon retirement and may owe taxes then, depending on the type of IRA chosen.
Explanation / Answer
Traditional IRA:
Amount invested per year $4,000
Tax Savings = 28% * $4,000 = $1,120
IRA earns 7% plus taxable investment earns 7% * (1 - 28%) = 5.04% after tax
Future Value Interest Factors for a One-Dollar Annuity Compouned at k% for n Periods:
FVIFAk,n = [(1 + k)^n- 1 ] / k
Total value of investment =
After tax future value of the IRA + Future value of the invested deductions (after tax)
=[ [ 4,000 * [(1 + 7%) ^ 25 -1 ] / 7 % ] * ( 1 - 28%) ] + [ 1,120 * [(1 + 5.04%) ^ 25 - 1] / 5.04%]
= 1,82,157.23 + 53,750.08 = 2,35,907.31
Total value of investment = $2,35,907.31
Roth IRA:
Total value of investment = Future value interest factor of annuity (FVIFA) of $4,000 at 7% for 25 years
= 4,000 * [(((1 + 7%) ^ 25) - 1) / 7%]
Total value of investment = 2,52,996.15
Recommendation:
The expected Future Value of the Roth IRA($2,52,996) is more than the expected Future Value of the traditional IRA plus the invested tax savings($2,35,907); so she should choose the Roth IRA.
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