The Mathematics of Money

(Darren Dugan) #1

Copyright © 2008, The McGraw-Hill Companies, Inc.



  1. Calculate the pension benefi t that would be paid for the following years of service and last 3 years’ salaries.


a. 40 years; $37,101; $36,544; $38,101
b. 7 years; $103,548; $107,626; $112,055


  1. Suppose that this pension plan allows its workers to begin receiving pension payouts as early as age 60. For each year
    below age 65, benefi ts are reduced by 2%. Calculate the pension benefi t that would be paid for the following years or
    service, last 3 years’ earnings, and retirement age: 28 years; $37,500; $38,425; $39,901; age 62.

  2. Suppose that this pension plan allows its workers to begin receiving pension payouts as late as age 72. For each year
    beyond age 65, benefi ts are increased by 1½%. Calculate the pension benefi t that would be paid for the following years
    or service, last 3 years’ earnings, and retirement age: 39 years; $52,600; $52,825; $53,011; age 69.


B. Defi ned Contribution Plans


  1. Mom and Pop’s Big Box Shoppes offers its employees a defi ned contribution plan. The company matches employee
    contributions at 60% up to 8% of salary.
    Randy earns $28,795 working for this company. How much will be deposited to his account per year if he contributes
    (a) nothing, (b) 5% of his salary, (c) 10% of his salary?

  2. A company offers its workers a defi ned contribution retirement plan, with 45% matching up to 9% of salary. If you take
    a job with this company, making a $39,400 annual salary, how much will be deposited to your account in your fi rst year
    if you contribute (a) nothing, (b) 6% of salary, (c) 12% of salary?

  3. Catskill University offers its faculty and staff a defi ned contribution retirement plan. If the employee contributes 4% of
    salary, the college will contribute 10% of salary to the plan. If an employee does not contribute anything, neither does
    the college. An employee may contribute more than 4%, but this will not increase the college’s contribution.
    Suppose that you work at Catskill U. and earn $34,750 this year. How much will be deposited to your account this year
    if your contributions to this plan total (a) $1,000, (b) $1,800 and (c) $4,000.


C. Vesting

To answer these questions, use the vesting schedules given in this section.


  1. For the 7-year step vesting schedule given in this section, what percent of the balance that comes from the employer’s
    contributions are vested if someone has completed service totaling (a) 3 years and 4 months, (b) 2 years and
    11 months, or (c) 6 years and 8 months? What percent of the balance that comes from the employee’s contributions
    are vested for each of these lengths of service?

  2. Bob has $10,350 in his defi ned contribution plan at work. Of that balance $7,573.25 comes from his own contributions
    and $2,776.75 comes from his employer’s. The plan uses the 7-year step vesting schedule given in this section of the text.
    How much of his plan balance would Bob keep if he leaves his job now, assuming he has 5 years and 3 months of service?

  3. Rita has $12,759.17 in her defi ned contribution retirement account at work. Of this amount, $4,387.15 comes from her
    contributions; the rest comes from her employer’s contributions. Her company uses the 7-year, 20% step vesting schedule.


Exercises 7.1 313
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