The Mathematics of Money

(Darren Dugan) #1
income throughout your retirement, despite the fact that none of us know how long we
have left on this earth. If you use this money to purchase an annuity, the insurer can provide
you with an income guaranteed for as long as you live. Purchasing an annuity contract is
one way to avoid the risk of outliving your money. Given the prevalence of 401(k)s as part
of retirement planning, it is likely that immediate annuities will be an increasingly impor-
tant financial product in the future, as retirees look to convert 401(k) balances into sources
of guaranteed lifetime income.

Other Retirement Accounts


IRAs and 401(k)s are by no means the only forms of retirement accounts in common
use. U.S. tax laws provide for a whole host of other accounts with similar purposes,
designed to meet the needs of self-employed people, smaller businesses, and other situ-
ations. These types of plans include Keogh plans, SIMPLE plans, and many others.
While these plans share many features with IRAs and 401(k)s, including tax advantages,
the details of these features and the limitations and regulations that apply to each type
of plan vary. While politicians always advocate simplifying things, and everyone agrees
that simplification is a good thing, the fact of the matter is that we can expect new types
of accounts to be created in the future, and the rules for existing accounts to be tinkered
with. Fortunately, retirement savings is big business, and major banks, brokers, mutual
fund companies, and other financial institutions that offer these types of account are
usually well-informed about the latest rules and regulations, and are prepared to assist
individuals and business owners in setting up and managing these accounts. A business
owner may also be able to obtain advice on the different options available from his
accountant.

EXERCISES 7.2


A. Traditional and Roth IRAs



  1. Suppose Andrew deposits $5,000 into an IRA, which earns an average rate of 8.25% for the next 40 years. Suppose
    that Andrew’s income tax rate bracket would require him to pay 35% in income taxes, whether paid today or in the
    future.


a. What is the future value of this deposit?
b. Suppose Andrew has a traditional IRA. Assuming that he is eligible to take this tax deduction, how much would he
save on his income taxes this year because of this deposit? Forty years from now, how much would this deposit be
worth after taxes are taken into account?
c. Suppose Andrew has a Roth IRA. How much would he be able to save on his income taxes this year because of
this deposit? Forty years from now, how much would this deposit be worth after taxes are taken into account?


  1. Bonnie is 28 years old. She has $3,500, which she is considering either depositing in a regular IRA or a Roth IRA. Suppose
    that her account will earn 8.4% on average from now until she is 65, at which point she will withdraw the money from her
    account. Her income level is such that she will pay 28% in income taxes, whether paid today or in the future.


a. If she puts this money into a traditional IRA, how much will she save in income taxes today? How much will she
pay when the money is withdrawn?
b. If she puts this money into a Roth IRA, how much will she save in income taxes today? How much will she pay in
income taxes when the money is withdrawn?

320 Chapter 7 Retirement Plans

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