Copyright © 2008, The McGraw-Hill Companies, Inc.
1.1 Simple Interest and the Time Value of Money 315E. Additional Exercises- Brad and Tracy have both started working, earning $37,500 per year. Both will receive salary increases of 4% each year
over the course of their careers.
Brad will continue working for the same company for 35 years and then retire. His company offers a defi ned benefi t
pension that pays 2% of fi nal salary for each year of service.
Tr acy will work for fi ve different companies, changing jobs every 7 years. At each of his jobs, there will be a defi ned
pension plan offering the same 2% of fi nal salary for each year of service that Brad’s company offers. Each of Tracy’s
employers will use 5-year cliff vesting.
a. Calculate Brad’s retirement benefi t.
b. Calculate the total of all the retirement benefi ts Tracy will receive from his fi ve jobs.
c. How does the total of Tracy’s retirement benefi ts compare to Brad’s?
d. Suppose that instead of defi ned benefi t plans, Brad and Tracy had had defi ned contribution plans. Assuming that all
of the employers in question offered the same percent contributions, and assuming that both Brad and Tracy earned
the same rate or return on their plan investments, how would Brad’s total account balance compare to Tracy’s?- Visit the Social Security website (www.socialsecurity.gov). On this site, you can fi nd an interactive tool that will allow you
to project Social Security benefi ts for someone on the basis of age and lifetime earnings.
a. Find the projected Social Security benefi t for Tracy, a female, presently 35 years of age, with no previous earnings,
assuming a $30,000 annual salary this year increasing by 4% each year until age 65.
b. Suppose that instead of this Social Security benefi t you instead were credited 6.5% of your annual salary into an
investment account. Using reasonable assumptions about how Tracy might invest this money and the rate of return
that might be expected for that asset allocation, calculate the future value that this investment account might
reach at age 65.
c. Suppose that once she reaches retirement, Tracy invests her money mainly in fi xed income investments and
withdraws her money at a rate that would allow the account to last 20 years. How does the payment from this plan
compare to the Social Security projection?
d. Aside from the size of the payments, what other signifi cant differences are there between traditional Social Security
and a privatized plan?
e. Suppose that instead of a 35-year old female, you did this exercise for someone of a different age and/or sex. How
would this affect the comparison between traditional and privatized options?Copyright © 2008, The McGraw-Hill Companies, Inc.
7.2 Details of Retirement Plans 3157.2 Details of Retirement Plans
In Section 7.1 we discussed the two main types of employer-sponsored retirement plans:
defined benefit and defined contribution plans. With defined benefit plans, the calcula-
tions that go into the funding and management of the plan that provides the promised
benefits are not the concern of the individual employee. For the employer they are so
complex that specialized professionals (called pension actuaries) must be hired to handle
these details, and so, not surprisingly, those details lie far beyond the scope of this book.
Defined contribution plans, though, are another matter entirely, and in this section we
will cover some of the main mathematical issues with these types of plans. At the same
time, retirement plans that are not tied to employment are also available, and we will also
consider those here.
To begin with, it should be stated that there does not have to be anything special about a
retirement account. Any money that someone saves and invests with the intent to use it to
fund their retirement can be considered a retirement account. Therefore, any of the future