A 25 - year - old with a dual BS/MS engineering degree accepts a job with a nati

Question

A 25

-

year

-

old with a dual BS/MS engineering degree accepts a

job with a national firm which has a required retirement age of

65. For simplicity, assume that the engineer stays through

retirement and that the average annual salary over the next 40

years is $96,000. The firm offers a

2

-

for

-

1 401(k) matching plan

(up to a maximum employee contribution of 6%). The chosen plan

offers a 3% expected rate of return after subtracting fees.

What will the engineer have in the plan at retirement?

What is the after

-

tax difference in income with and without the 401(k)

deduction?

Explanation / Answer

Annual Salary = $96000

Employee's contribution to 401(k) = 6% of $96000 = $5760

Employer's Contribution = $5760

Total annual investment = $11520

Value of investment at the end of 40th year = $11520

Formula for future value of annuity = Payment *( (1+ rate)number of periods -1)/ rate

= $11520 * (( 1+3%)40- 1) /0.03 = $868622.5121

At retirement, engineer wil have $868622.51 in savings

----------------------------------------------------------------

Taxable income with 401(k) = $96000 - $5760 = $90240

Tax liability = $5226.25 + 25% of ($90240-$40250) = $17723.75

Taxable income without 401(k) = $96000

Tax liability = $18713.75 + 28% of ($96000- $94200) = $19217.72

After tax difference in income is = $19217.72 - $17723.75 = $1493.97

Annual taxable income between Annual withholding additional withholding over this amoount 40250-94200 5226.25 plus 25% of income over 40250 94200-193950 18713.75 plus 28% of income over 94200

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