322 Chapter 7 Retirement Plans
- Dan has just retired and he has $743,500 in his 401(k) account. He plans to take equal monthly payments from this
account, with the idea of making his money last for 25 years. Assuming that he earns 4.8% on his account over this
time period, how much can he withdraw each month? - Suppose Jenny will retire in 19 years. She presently has $175,936 in her 401(k) account. When she retires, she plans
to take equal monthly withdrawals of $3,500 from her 401(k) and have her money last for 20 years. If her account will
earn 7.25% compounded monthly until she retires and 3.75% while she is retired, calculate (a) the amount she needs
to have in her account at retirement and (b) the amount she needs to deposit to her 401(k) each month in order to
reach this goal.
322 Chapter 7 Retirement Plans
7.3 Assessing the Effect of Infl ation
Many of the financial calculations we have done have dealt with long-term goals, such as
figuring out how much you need to set aside each month to be a millionaire in retirement
40 years from now. While our work has been mathematically correct, we have ignored a
very important practical concern: the impact of inflation.
Loosely speaking, inflation is the tendency of prices to rise over time. While there is
nothing that requires this to happen, it is common knowledge that prices do tend by and
large to go up over time. Though no one likes higher prices, inflation is not entirely a bad
thing, at least when the rate of inflation is moderate or low. As long as prices do not rise too
far or too fast we hardly even notice inflation in our daily lives.
Of course, when prices rise a lot, inflation is much harder to ignore and can be devastat-
ing to both individuals’ personal finances and to the economy as a whole. An inflation rate
of, say, 25% would mean that prices would double roughly every three years. Your earn-
ings would have to rise by 25% annually, and your savings would have to grow at that rate,
just to keep pace with the rise of prices. Yet even though this would be a very high rate, at
least compared to the inflation rates historically seen in the United States, inflation rates
can, and have, gone much higher in other places. Germany experienced devastating infla-
tion rates after the First World War, and the economic insecurities they caused are often
cited as a contributing factor in the rise of Adolf Hitler. Similarly awful inflation has been
experienced in many different times and places, often in the aftermath of war or economic
or political upheavals.^4
While hopefully we will never have the pleasure of experiencing inflation on anywhere
near that scale, even tame, barely-noticeable inflation rates can be significant over long
periods of time. In modern history the inflation rate in the United States has varied quite a
bit, but has averaged out to somewhere in the neighborhood of 3.5%.^5 This has not been a
steady rate from year to year; in the 1970s and early 1980s the rate of inflation ran much
higher, while in the 1990s inflation was nearly nonexistent, and some economists even
worried about the possibility of deflation, prices dropping overall rather than rising.
In the near term, inflation running at a 3.5% average is hardly even noticeable. But
over the long term, the cumulative effect of compounding inflation can really add up. For(^) example, assuming that a 3.5% rate of inflation continued for the next 40 years, a candy bar
that costs 65 cents today would cost a whopping $2.57! So if you set aside 65 cents in your
(^4) What is often regarded as the all-time world record for infl ation occurred in Hungary in the wake of the Second World
War. During this period, by some estimates the infl ation rate reached a staggering 41.9 quadrillion percent per year, or
41,900,000,000,000,000%. With this infl ation rate, prices would double on average every 15 hours.
(^5) There is some controversy about how to measure the real rate of infl ation, mainly because prices for all things do not
rise at a uniform rate. The “infl ation rate” is an attempt to measure how fast prices are rising overall, but your overall
may not be the same as mine. If the prices of things that you buy are rising more quickly (or slowly) than the prices of
things you don’t, the infl ation rate as far as you are concerned will be higher (or lower) than the overall rate.