Editing Retirement (section)

==Saving for retirement==
[[File:20230331 Average retirement savings account balances and median net worth, by age, US.svg|thumb|In the U.S., average balances of retirement accounts, for households having such accounts, exceed median net worth across all age groups. For those 65 and over, 11.6% of retirement accounts have balances of at least $1 million, more than twice that of the $407,581 average (shown). Those 65 and over have a ''median'' net worth of about $250,000 (shown), about a quarter of the group's ''average'' (not shown).<ref name=WSJ_20230331>{{cite news |last1=Dagher |first1=Veronica |last2=Tergesen |first2=Anne |last3=Ettenheim |first3=Rosie |title=Here's What Retirement Looks Like in America in Six Charts |url=https://www.wsj.com/articles/retirement-charts-social-security-savings-health-efa1962b |work=The Wall Street Journal |date=March 31, 2023 |archive-url=https://web.archive.org/web/20230331093530/https://www.wsj.com/articles/retirement-charts-social-security-savings-health-efa1962b |archive-date=March 31, 2023 |quote=(For Average household retirement savings account balance:) Estimates of 401(k), IRA, Keogh and other defined contribution account balances based on 2019 data. Source: Employee Benefit Research Institute. . . . (For median net worth:) Source: Federal Reserve. |url-status=live }}</ref>]]
Overall, income after retirement can come from state pensions, occupational pensions, private savings and investments (private pension funds, owned housing), donations (e.g., by children), and social benefits.<ref>Eurofound, Income from work after retirement in the EU (2012) http://www.eurofound.europa.eu/pubdocs/2012/59/en/2/EF1259EN.pdf</ref> In some countries an additional lump sum is granted, according to the years of work and the average pay; this is usually provided by the employer. On a personal level, the rising cost of living during retirement is a serious concern to many older adults. [[Health care costs]] play an important role.

Provision of state pensions is a significant drain on a government's budget. As life expectancy increases and the health of older people improves with medical advances, the age of entitlement to a pension has been increasing progressively since about 2010.

Older people are more prone to sickness, and the cost of health care in retirement is large. Most countries provide universal health insurance coverage for seniors, although in the United States many people retire before they become eligible for [[Medicare (United States)|Medicare]] health cover at 65 years of age.

===Calculators===

A useful and straightforward calculation can be done if it is assumed that interest, after expenses, taxes, and inflation is zero. Assume that in real (after-inflation) terms, one's salary never changes over ''w'' years of working life. During ''p'' years of pension, one has a living standard that costs a replacement ratio ''R'' times as much as one's living standard in working life. The working life living standard is one's salary minus the proportion of salary Z that should be saved. Calculations are per unit salary (e.g., assume salary = 1).

Then after ''w'' years work, retirement age accumulated savings = ''wZ''. To pay for pension for ''p'' years, necessary savings at retirement = ''Rp(1-Z)''

Equate these: ''wZ'' = ''Rp''(''1-Z'') and solve to give ''Z'' = ''Rp'' / (''w + Rp''). For example, if ''w'' = 35, ''p'' = 30 and ''R'' = 0.65, a proportion ''Z'' = 35.78% should be saved.

Retirement calculators generally accumulate a proportion of salary up to retirement age. This shows a straightforward case, which nonetheless could be practically useful for optimistic people hoping to work for only as long as they are likely to be retired.

For more complicated situations, there are several online retirement calculators on the Internet. Many retirement calculators project how much an investor needs to save, and for how long, to provide a certain level of retirement expenditures. Some retirement calculators, appropriate for safe investments, assume a constant, unvarying rate of return. Monte Carlo retirement calculators take volatility into account and project the probability that a particular plan of retirement savings, investments, and expenditures will outlast the retiree. Retirement calculators vary in the extent to which they take taxes, social security, pensions, and other sources of retirement income and expenditures into account.

The assumptions keyed into a retirement calculator are critical. One of the most important assumptions is the assumed rate of real (after inflation) investment return. A conservative return estimate could be based on the real yield of [[Inflation-indexed bond]]s offered by some governments, including the United States, Canada, and the United Kingdom. The TIP$TER retirement calculator projects the retirement expenditures that a portfolio of inflation-linked bonds, coupled with other income sources like Social Security, would be able to sustain. Current real yields on United States Treasury Inflation Protected Securities (TIPS) are available at the US Treasury site. Current real yields on Canadian 'Real Return Bonds' are available at the Bank of Canada's site. As of December 2011, US Treasury inflation-linked bonds (TIPS) were yielding about 0.8% real per annum for the 30-year maturity and a noteworthy slightly negative real return for the 7-year maturity.

[[File:Work 40 retire 20.jpg|right|250px]]
Many individuals use "retirement calculators" on the Internet to determine the proportion of their pay they should be saving in a tax advantaged-plan (e.g., IRA or 401-K in the US, RRSP in Canada, personal pension in the UK, superannuation in Australia).
After expenses and any taxes, a reasonable (though arguably pessimistic) long-term assumption for a safe real rate of return is zero. So in [[Real versus nominal value (economics)|real terms]], interest does not help the savings grow. Each year of work must pay its share of a year of retirement. For someone planning to work for 40 years and be retired for 20 years, each year of work pays for itself and for half a year of retirement. Hence, 33.33% of pay must be saved, and 66.67% can be spent when earned. After 40 years of saving 33.33% of pay, we have accumulated assets of 13.33 years of pay, as in the graph. In the graph to the right, the lines are straight, which is appropriate given the assumption of a zero real investment return.

The graph above can be compared with those generated by many retirement calculators. However, most retirement calculators use nominal (not "real" dollars) and therefore require a projection of both the expected inflation rate and the expected nominal rate of return. One way to work around this limitation is to, for example, enter "0% return, 0% inflation" inputs into the calculator. The Bloomberg retirement calculator gives the flexibility to specify, for example, zero inflation and zero investment return and to reproduce the graph above. The MSN retirement calculator in 2011 has as the defaults a realistic 3% per annum inflation rate and optimistic 8% return assumptions; consistency with the December 2011 US nominal bond and inflation-protected bond market rates requires a change to about 3% inflation and 4% investment return before and after retirement.

Ignoring tax, someone wishing to work for a year and then relax for a year on the same living standard needs to save 50% of pay. Similarly, someone wishing to work from age 25 to 55 and be retired for 30 years till 85 needs to save 50% of pay if government and employment pensions are not a factor and if it is considered appropriate to assume a zero real investment return. The problem that the lifespan is not known in advance can be reduced in some countries by the purchase at retirement of an inflation-indexed [[life annuity]].

===Size of lump sum required===

To pay for pension, assumed for simplicity to be received at the end of each year, and taking discounted values in the manner of a [[net present value]] calculation, the ideal lump sum available at retirement should be:

:(1 – z<sup>prop</sup> ) R <sup>repl</sup>  S {(1+ i<sup>real</sup> ) <sup>−1</sup>+(1+ i<sup>real</sup> ) <sup>−2</sup>   +...  ....+ (1+ i<sup>real</sup> ) <sup>−p</sup>} = (1-z<sup>prop</sup> )  R <sup>repl</sup>   S  {(1 – (1+i<sup>real</sup>)<sup>−p</sup>   )/i<sup>real</sup>}

Above is the standard mathematical formula for the sum of a [[geometric series]]. (Or if i<sup>real</sup> =0 then the series in braces sums to p since it then has p equal terms). As an example, assume that S=60,000 per year and that it is desired to replace R<sup>repl</sup>=0.80, or 80%, of pre-retirement living standard for p=30 years. Assume for current purposes that a proportion z <sup>prop</sup>=0.25 (25%) of pay was being saved. Using i<sup>real</sup>=0.02, or 2% per year real return on investments, the necessary lump sum is given by the formula as (1–0.25)*0.80*60,000*annuity-series-sum(30)=36,000*22.396=806,272 in the nation's currency in 2008–2010 terms. To allow for inflation in a straightforward way, it is best to talk of the 806,272 as being '13.43 years of retirement age salary'. It may be appropriate to regard this as being the necessary lump sum to fund 36,000 of annual supplements to any employer or government pensions that are available. It is common to not include any house value in the calculation of this necessary lump sum, so for a homeowner the lump sum pays primarily for non-housing living costs.

===Size of lump sum saved===

At retirement, the following amount will have been accumulated:

:z<sup>prop</sup> S {(1+ i <sup>rel to pay</sup> )<sup>w-1</sup>+(1+ i <sup>rel to pay</sup> )<sup>w-2</sup>   +...  ....+ (1+ i <sup>rel to pay</sup> )+ 1 }

:&nbsp;= z<sup>prop</sup>  S  ((1+i <sup>rel to pay</sup>)<sup>w</sup>- 1)/i <sup>rel to pay</sup>

===Equate and derive necessary saving proportion===

To make the accumulation match with the lump sum needed to pay pension:

:z<sup>prop</sup>  S  (((1+i <sup>rel to pay</sup> )) <sup>w</sup>  – 1)/i <sup>rel to pay</sup>   = (1-z<sup>prop</sup> )  R <sup>repl</sup>   S  (1 – ((1+i <sup>real</sup>)) <sup>−p</sup> )/i<sup> real </sup>

Bring z<sup>prop</sup> to the left hand side to give the answer, under this rough and unguaranteed method, for the proportion of pay that should be saved:

:z<sup>prop</sup> = R <sup>repl</sup>    (1 – ((1+i <sup>real</sup> )) <sup>−p</sup> )/i <sup>real</sup>  /  [(((1+i <sup>rel to pay</sup> )) <sup>w</sup> – 1)/i <sup>rel to pay</sup>  + R <sup>repl</sup>   (1 – ((1+i <sup>real</sup> )) <sup>−p</sup> )/i <sup>real</sup>  ] (Ret-03)

Note that the special case i <sup>rel to pay</sup> =0 =  i <sup>real</sup> means that the geometric series should be summed by noting that there are p or w identical terms and hence z <sup>prop</sup> = p/(w+p). This corresponds to the graph above with the straight line real-terms accumulation.

===Sample results===
The result for the necessary z<sup>prop</sup> given by (Ret-03) depends critically on the assumptions made. As an example, one might assume that price inflation will be 3.5% per year forever and that one's pay will increase only at that same rate of 3.5%. If a 4.5% per year nominal rate of interest is assumed, then (using 1.045/1.035 in [[Real versus nominal value (economics)|real terms]]) pre-retirement and post-retirement net interest rates will remain the same, i<sup>rel to pay</sup> = 0.966 percent per year and i<sup>real</sup> = 0.966 percent per year. These assumptions may be reasonable in view of the market returns available on [[inflation-indexed bond]]s, after expenses and any tax. Equation (Ret-03) is readily coded in Excel and with these assumptions gives the required savings rates in the accompanying picture.

===Monte Carlo: Better allowance for randomness===
Finally, a newer method for determining the adequacy of a retirement plan is [[Monte Carlo simulation]]. This method has been gaining popularity and is now employed by many financial planners.<ref>{{cite web|url=http://www.capitalspectator.com/WM/2007/03/a_sure_bet_1.html|archive-url=https://web.archive.org/web/20070611162405/http://www.capitalspectator.com/WM/2007/03/a_sure_bet_1.html|url-status=dead|archive-date=11 June 2007|title=A SURE BET? (Wealth Manager)|date=11 June 2007}}</ref> Monte Carlo retirement calculators<ref>{{cite web|url=https://vestingpoint.com/|archive-url=https://web.archive.org/web/20110202101013/https://vestingpoint.com/|url-status=usurped|archive-date=2 February 2011|title=Retirement calculator – easy, comprehensive, informative|date=2 February 2011}}</ref><ref>[http://www.flexibleRetirementPlanner.com Online Monte Carlo Retirement Planner<!-- Bot generated title -->].</ref> allow users to enter savings, income and expense information and run simulations of retirement scenarios. The simulation results show the probability that the retirement plan will be successful.