318 Chapter 7 Retirement Plans
though, that she should at least contribute the full 6% that her company will match, since
the matching provides a bonus of 75 cents on each dollar.
The history of the 401(k) plan is interesting. IRAs were intentionally created to offer
people encouragement and incentives to invest for their own retirement. On the other hand,
401(k)s came about when someone noticed a loophole in the tax laws that would allow
for this sort of account. The strange name 401(k) comes from the section of the tax code
where this loophole was found. From this humble and accidental origin, though, 401(k)
plans have grown to become a major part of many companies’ benefit plan offerings, and a
cornerstone of retirement planning.Example 7.2.3 Curt is 24 years old, and he has just started a new job, which offers
a 401(k) plan. He will be making $31,000 per year. Looking to the future, Curt is
wondering what percent of his salary he should contribute to the 401(k) if he wants
to have $750,000 in this account when he reaches age 65. He is paid biweekly, his
company does not offer any matching, and he expects that his investments in the plan
can earn 10%.We can look at Curt’s 401(k) contributions as an annuity designed to build up the desired
$750,000 future value. Recall that biweekly works out to 26 times per year.FV PMT s −n| (^) i
$750,000 PMT s 1066 0.10⁄ 26
$750,000 PMT(15,305.57734)
PMT $49.00
Curt’s biweekly pay will be $31,000/26 $1,192.31. A $49.00 contribution amounts to
$49.00/$1,192.31 4.11%.
Of course, these sorts of calculations can’t be taken too literally. Using an annuity assumes
that Curt’s contributions remain constant over the next 41 years, which may not be realistic.
The $49.00 is 4.11% of his current salary, but one would hope that Curt would get a raise at
some point over the next 41 years! The 10% rate of return assumed is a (hopefully, educated)
guess, and the $750,000 figure may or may not be enough to meet Curt’s needs in retirement.
These figures ignore the impact of inflation as well. Section 7.3 will address some of these
concerns mathematically, but even with them, this calculation does allow Curt to get a ball-
park sense of just how much is reasonable to be contributing. It would not be reasonable
for Curt to conclude that he should sign up to contribute exactly 4.11% of his salary to the
401(k)—taking this figure exactly and literally ignores all of the factors we’ve mentioned.
It would, though, be reasonable for him to conclude that, to achieve his goal, signing up to
contribute 4 or 5% would be a good idea. (Of course, more wouldn’t hurt either.)
These sorts of calculations are more complicated when an employer match is involved,
as the following two examples will show.
Example 7.2.4 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 that her investments can
earn 8½%. Her employer matches her contributions 50% up to 8% of salary. How much
of her salary should she contribute?
Following the approach of the prior example gives:
FV PMT s −n| (^) i
$250,000 PMT s 780 0.085⁄ 26
$250,000 PMT(3,595.324968)
PMT $69.53
This total includes both her and her employer’s contributions. How much does she need to
contribute herself? The employer match means that the funds going into the 401(k) will be
150% of her own contributions, so: