The Mathematics of Money

(Darren Dugan) #1

330


CHAPTER 7


SUMMARY


Topic Key Ideas, Formulas, and Techniques Examples


Defi ned Benefi t Plans, p. 307 • The benefi ts paid under a defi ned benefi t plan
are determined by a formula specifi ed in the
plan documents


  • Benefi t formulas typically take into account
    years of service, average salary over some time
    period, and age at retirement.


A pension plan provides 2%
of fi nal 3-year average salary
for each year of service on
retirement at age 65. Jelena
retired at 65 with 28 years
of service. Her last 3 years’
earnings were $37,650,
$39,525 and $40,187.
Calculate her pension benefi t.
(Example 7.1.2)

Defi ned Contribution
Plans, p. 309


  • Defi ned contribution plans do not guarantee
    any specifi c income amount.

  • The employer makes contributions to each
    employee’s account based on a set formula.

  • Employer contributions may be based
    on matching a percent of the employee’s
    contribution.


Daxxilon Digital Devices
matches 75% of each
employee’s plan contributions
up to a 10% maximum. Hamid
earns $60,000. How much will
be deposited to his account
if he contributes 5% of his
earnings? 15%?
(Example 7.1.5)

Vesting, p. 309 • If you leave a job before retirement, the amount
of benefi ts you keep is determined by a vesting
schedule.


  • The schedule specifi es the percent kept on the
    basis of the years of service completed.

  • Account values that come from your own
    contributions are always yours to keep.


Kelly is leaving her job where
she has been working for 3½
years. The company uses
7-year step vesting. Her
contributions have grown to
$5,622.16 and the company’s
have grown to $4,810.33. Find
her vested balance.
(Example 7.1.7)

IRAs and Roth IRAs, p. 316 • Money deposited to a traditional IRA may be
tax-deductible and grows tax-deferred. It is
taxed when withdrawn.


  • Money deposited to a Roth IRA is not tax-
    deductible. Withdrawals are not subject to
    income tax.


Sarah has $3,000 to invest
in an IRA. She expects this
money will earn 9% and will
not withdraw it for 40 years.
Assuming she will pay a 30%
rate for state and federal
taxes, how much will she have
after tax if she invests in (a)
a Roth IRA or (b) a traditional
IRA?
(Example 7.2.1)

401(k)s, p. 317 • 401(k) plans are retirement savings accounts
offered as an employee benefi t.


  • They are a type of defi ned contribution plan

  • 401(k)s often include an employer match of
    contributions.


Nancy earns $26,000 per year
and is paid biweekly. She
wants to have $250,000 in
her 401(k) 30 years from now
and thinks her investments
will earn 8½%. Her employer
matches contributions 50%
up to 8%. How much of her
salary should she contribute
to reach this goal?
(Example 7.2.4)

(Continued)
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