The Mathematics of Money

(Darren Dugan) #1
B. 401(k) Plan Projections

Assume that all employees in these examples are paid biweekly (26 times per year).


  1. LaNetta is 28 years old. She has just taken a new job at a company that offers a 401(k) plan with a 50% employer
    match up to 9% of salary. She will be earning $28,500 per year.
    If her 401(k) investments earn 7%, and she contributes 5% of her income, how much would her 401(k) balance grow to
    in 35 years. (Assume that her income remains constant at $28,500 per year.)

  2. Kris’s company offers a 401(k) plan with no employer match. Kris would like to have $500,000 in his account in
    40 years. He makes $33,000 per year. He believes his investments can earn 6.5%. (a) How much should he be
    depositing with each paycheck? (b) To achieve this goal, what percent of his salary should he be contributing to this
    plan? (Assume his annual income does not change.)


The Winterburg Central School District offers its employees a 401(k) plan with a 40% employer match up to 10%. Walter has
just taken a job with the district, earning $35,700 per year. Exercises 4 to 7 are based on Walter and this 401(k) plan.


  1. Walter would like to have $250,000 in his 401(k) plan when he retires in 37 years. If his investments can earn 7.25%,
    what percent of his salary would he want to contribute?

  2. Suppose that Walter decides that he should aim higher, and sets his target to be $500,000. What percent of salary
    would he want to contribute then?

  3. Suppose that Walter sets his sights even higher and decides to aim for $750,000. What percent of his salary would he
    want to contribute then?

  4. Suppose that Walter starts thinking that he wants to set an even higher goal, in hopes of either retiring early and/
    or being able to afford a higher standard of living when he does. What percent of his salary would Walter want to
    contribute if he sets a goal of $1,500,000.


C. Grab Bag


  1. Eriko earns $45,755 per year. She contributes 8% of her income to her 401(k) plan at work. In her tax bracket, she
    would pay 37% of her income in state and federal income taxes.


a. How much is she saving this year on her taxes by making these 401(k) plan contributions?
b. Suppose that instead of contributing to her 401(k) plan, she decides instead to deposit the same amount of money
to a Roth IRA. What would her tax savings be this year if the money went into the Roth instead?
c. Eriko has projected that her retirement account deposits will have grown to $318,902 by the time she retires. Assuming
the same 37% tax rate, what would the after-tax value of her account be if the money is in a 401(k)? In a Roth IRA?
d. Suppose that Eriko’s company offers a 75% match up to 10% of salary, how would this affect her decision of
whether to stick with the 401(k) or instead switch to a Roth IRA?

D. Additional Exercises


  1. Suppose that Walter (from Exercises 4 to 7) set his future value goal at $1,000,000. What percent of his salary would
    he want to contribute to achieve this goal?


Exercises 7.2 321

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