Retirement planning needs to consider this aspect too. In an earlier example the size of the nest egg was found based on the idea of retiring on $40,000 per year. But again the $40,000 is not in today's dollars. At the time of retirement this amount is only $12,262 in today's money and this value will decrease every year into retirement!

We note once again the modeling aspect of this section due to unknowns in returns on investments and inflation. Each problem worked has used an underlying assumption of a constant percentage return on investment; in truth, investments often involve the buying of a portfolio of shares whose success depends on the stock market. It is likely that such returns will vary from year to year.

If this section has painted a gloomy picture, we end with a glimmer of hope. Firstly there may be tax breaks in saving for retirement. Any money (up to some limit) put into a (traditional) retirement account (but not a Roth which has different advantages) is tax deductible. Taxation occurs only as income on its withdrawal during retirement. This has the advantage of allowing a greater amount to accrue with interest over the years before it is taxed. Also employment, at least in larger companies or with government agencies, may come with a retirement plan in which the company matches an employee's retirement contribution (an employer sponsored 401(k) retirement savings plan) so that the monthly amounts seen in the examples above may be halved when thinking about affordability

4B.1 How much is in a savings plan after 20 years if $200 is deposited each month at 3.2% APR compounded monthly?

4B.2 How much must be deposited each quarter in a savings plan earning 4% APR compounded monthly if the plan is to accrue to $300,000 after 25 years?

4B.3 Polly invests $300 each month in a retirement account that pays 6% APR compounded monthly. What is the value of her retirement account in 30 years? If she continues to earn 6% on her nest egg, what is her annual retirement income?

The consumer price index is a useful index of inflation, and may be used to adjust the limits of each tax bracket for the upcoming year. Nevertheless the CPI has its critics. A lot of things are used in the determination of the value of the index at a given time take a look at the latest (May 2016) values for a few of the categories listed under the Consumer Price Index Summary http://www.bls.gov/news.release/cpi.t01.htm - and youll see it is easy to argue against the balance of the categories used. Note that 100 is the base CPI value from December 1982. The May 2016 CPI is that listed under unadjusted All Items; values higher than this number have increased more than average since December 1982; those less than this have increased less than average. Consider the effects of inflation on retirees. (We painted a pessimistic picture in Section 4B one example showed that $40,000 per year in 40 years time equates to just $12,262 in todays dollars.) It should be clear that some categories used in the CPI calculation are less of an issue for retired folks:

a) List 3 categories whose index is lower (better) than the overall CPI and 3 categories that are higher (worse) than the overall CPI. Be sure to state the overall CPI and the values of the categories you choose.

b) Writing in Mathematics. Write a short paragraph to discuss whether the retirement gloom shown in 4B was pessimistic or a reality. Are any of the individual categories that are much worse than the overall likely to be a major expense for retirees?