# Retirement

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**Retirement** is the point where a person stops employment completely. A person may also semi-retire and keep some sort of retirement job, out of choice rather than necessity. This usually happens upon reaching a determined age, when physical conditions don't allow the person to work any more (by illness or accident), or even for personal choice (usually in the presence of an adequate pension or personal savings). The retirement with a pension is considered a right of the worker in many societies, and hard ideological, social, cultural and political battles have been fought over whether this is a right or not. In many western countries this right is mentioned in national constitutions.

## Retirement age

In most countries, the idea of a fixed retirement age is of recent origin, being introduced during the 19th and 20th centuries - before then, the absence of pension arrangements meant that most workers continued to work until death, or relied on personal savings or the support of family or friends. Nowadays most developed nations have systems to provide pensions on retirement in old age, which may be sponsored by employers or the state. In many poorer countries, support for the old is still mainly provided through the family.

The retirement age varies from country to country but it is generally between 55 and 70. In some countries this age is different for males and females. Sometimes certain jobs, the most dangerous or fatiguing ones in particular, have an earlier retirement age.

In the United States, while most view 65 as normal retirement age, many retire before then, sometimes with contributory causes such as job-loss, disability or wealth. However, the Old Age Survivors Insurance or OASI, better known as the Social Security system has age 62 as the earliest retirement age. Normal retirement age for Social Security has historically been age 65 to receive unreduced benefits, but it is gradually increasing to age 67. For those turning 65 in the year 2008 full benefits will be payable beginning at age 66. ^{[1]} Police officers in the United States are typically allowed to retire at half pay after only 20 years of service or three-quarter pay after 30 years, allowing people to retire in their early forties or fifties.^{[2]}

In 2007, retirement age for teachers in France is thirty eight years after employment and age 50 for train engineers ^{[3]} on the SNCF, the national railway.

The retirement age in India for public sector employees is enhanced from 58-60 years in July 2007. In Malaysia the retirement age has just recently been raised from 55 years to 56 years.

Many politicians, scientists, lawyers, television anchors, and professors still work well into their 70s, however some actors, models, athletes, and musicians only work until their 30s.

Military members of the US Armed Forces may elect to retire after 20 years of active duty. Their retirement pay (not a pension since they can be involuntarily called back to active duty at any time) is calculated on total number of years on active duty, their final pay grade and the retirement system in place when they entered service. Allowances such as housing and subsistence are not used to calculate a member's retired pay. Members awarded the Medal of Honor qualify for a separate stipend, regardless of the years of service. There is a federally mandated cap of 75% of their final base pay in all cases. Military members in the reserve and US National Guard have their retirement based on a point system. [citation needed]

## Support and funds

Retired workers then support themselves either through pensions or savings. In most cases the money is provided by the government, but sometimes granted only by private subscriptions to mutual funds. In this latter case, subscriptions might be compulsory or voluntary. In some countries an additional "bonus" is granted *una tantum* (once only) in proportion to the years of work and the average wages; this is usually provided by the employer.

The financial weight of provision of pensions on a government's budget is often heavy and is the reason for political debates about the retirement age. The state might be interested in a later retirement age for economic reasons.

The cost of health care in retirement is large, because people tend to be ill more frequently in later life. Increasing numbers of older people, combined with an increase in the cost of healthcare, has led to the funding of post-retirement health care becoming a political issue. There is then pressure to reform healthcare systems to contain costs, or find new sources of funding.

On a personal level, the rising cost of living during retirement is a serious concern to many older adults.

### Retirement calculators

Many individuals use 'retirement calculators' on the Internet to determine the proportion of their pay which they should be saving in a tax advantaged-plan (eg IRA or 401-K in the US, RRSP in Canada, personal pension in the UK). The assumptions keyed into the calculator are critical, especially the assumed rate of real (after inflation) investment return. In 2008, US Treasury inflation-linked bonds (TIPS) are yielding a low 1.5% per annum; the equivalent UK 'indexed' bonds are yielding less than 1%, and Canadian 'Real Return bonds' are yielding about 1.8% per annum.

Any spreadsheet or retirement calculator should be able to pass the test of giving the correct savings rate for a simple case. Assume that pay rises roughly as fast as price inflation. Note also that government 20-year inflation-indexed bonds in 2008 are yielding only about 1.0% to 2.0% per year, real, depending on the country. Current United States real yields are available at the ustreas.gov site 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 terms, interest doesn't 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 to 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. The asset accumulation and use is as shown in the diagram, where the lines are straight in this situation of zero real yield. This is straightforward if one assumes zero inflation and zero investment return: after 40 years of saving 33.33% of pay we have accumulated assets of 13.33 years of pay, as in the graph. Somewhat less obvious is the fact that the graph is also appropriate to any case of zero real investment return.

This graph can be compared with those generated by many retirement calculators, though it should be noticed that if non-zero inflation is specified in using a calculator then the calculator will usually produce a graph in nominal (not 'real') dollars, so the lines will not be straight. A workaround is to, for example, change a '4% return, 4% inflation' assumption to '0% return, 0% inflation' in the calculator. This should give substantially the same results in real terms. The MSN retirement calculator in 2008 cannot be changed from an assumed 3% per annum inflation rate, so one would set an investment return assumption of 3%. The Bloomberg retirement calculator gives the flexibility to specify, for example, zero inflation and zero investment return and to reproduce the graph given here. The retirement calculator provided at the AARP's site gives guidance on choice of assumptions.

Someone wishing to work from age 25 to 55 and to 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.

### Retirement calculations

For most people, employer pensions, government pensions and the tax situation in their country are important factors, typically taken account of in calculations by actuaries. Ignoring those significant nation-specific factors but not necessarily assuming zero real interest rates, a 'not to be relied upon' calculation of required personal savings rate z^{prop} can be made using a little mathematics. ^{[4]}It helps to have a dimly-remembered acquaintance with geometric series, maybe in the form

1+r+r^{2}+ r^{3} + + r ^{n-1} = (1-r^{n})/(1-r)

You work for w years, saving a proportion z^{prop} of pay at the end of each year. So the after-savings purchasing power is (1-z^{prop}) of pay while you are working. You need a pension for p years. Let’s say that at retirement you are earning S per year and require to replace a ratio R^{repl} of your pre-retirement living standard. So you need a pension of (1 – z^{prop} ) R^{repl} S, indexed to price inflation.

Let’s assume that the investments, after price inflation f^{price}, earn a real rate i^{real} in real terms where

(1+ i^{real} ) = ((1+i^{nominal}))/((1+f^{price} ) ) (Ret-01)

Let’s assume that the investments, after wage inflation f^{pay}, earn a real rate i ^{rel to pay} where

(1+ i ^{rel to pay} ) = ((1+i^{nominal}))/((1+f^{pay} ) ) (Ret-02)

### Size of lump sum you need: Is a million enough?

To pay for your 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, you need a lump sum available at retirement of:

(1 – z^{prop} ) R ^{repl} S {(1+ i^{real} ) ^{-1}+(1+ i^{real} ) ^{-2} +… ….+ (1+ i^{real} ) ^{-p}}

= (1-z^{prop} ) R ^{repl} S {(1 – (1+i^{real})^{-p} )/i^{real}}

Above we have used the standard mathematical formula for the sum of a geometric series. (Or if i^{real} =0 then the series in curly parentheses 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^{repl}=0.80, or 80%, of pre-retirement living standard for p=30 years. Assume for current purposes that a proportion z ^{prop}=0.25 (25%) of pay was being saved. Using i^{real}=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 straighforward 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

Will you have saved enough at retirement? Use our necessary but unrealistic assumption of a constant after-pay-rises rate of interest. At retirement you have accumulated

z^{prop} S {(1+ i ^{rel to pay} )^{w-1}+(1+ i ^{rel to pay} )^{w-2} +… ….+ (1+ i ^{rel to pay} )+ 1 }

= z^{prop} S ((1+i ^{rel to pay})^{w}- 1)/i ^{rel to pay}

### Equate and derive necessary saving proportion

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

z^{prop} S (((1+i ^{rel to pay} )) ^{w} - 1)/i ^{rel to pay} = (1-z^{prop} ) R ^{repl} S (1 – ((1+i ^{real})) ^{-p} )/i^{ real }

Bring z^{prop} to the left hand side to give our answer, under this rough and unguaranteed method, for the proportion of pay that we should be saving:

z^{prop} = R ^{repl} (1 – ((1+i ^{real} )) ^{-p} )/i ^{real} / [(((1+i ^{rel to pay} )) ^{w} - 1)/i ^{rel to pay} + R ^{repl} (1 – ((1+i ^{real} )) ^{-p} )/i ^{real} ] (Ret-03)

You are encouraged to download the use-at-your-own-financial-risk spreadsheet. The results in the spreadsheet can be seen to make sense. For example, working for 5 years and drawing a pension for 5 years requires you to save almost half your pay, with interest helping only a little.

Note that the special case i ^{rel to pay} =0 = i ^{real} means that we instead sum the geometric series by noting that we have p or w identical terms and hence z ^{prop} = p/(w+p). This corresponds to our graph above with the straight line real-terms accumulation.

### Sample Results

The result for the necessary z^{prop} given by (Ret-03) depends critically on the assumptions that you make. As an example, you might assume that price inflation will be 3.5% per year forever and that your pay will increase only at that same rate of 3.5%. If you assume a 4.5% per year nominal rate of interest, then (using 1.045/1.035 in real terms ) your pre-retirement and post-retirement net interest rates are the same, i^{rel to pay} = 0.966 percent per year and i^{real} = 0.966 percent per year. These assumptions may be reasonable in view of the market returns available on inflation-indexed bonds, 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.^{[5]} A Monte Carlo retirement calculator ^{[6]} allows 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.

## Early retirement

Early retirement can be at any age, but is generally before the age (or tenure) needed for eligibility for support and funds from government or employer-provided sources. Thus, early-retirees rely on their own savings and investments to be initially self-supporting, until they start receiving such external support. Early retirement is also a euphemistic term for accepting termination of employment before retirement age as part of the employer's labor force rationalization. In this case, a monetary inducement may be involved.

### Savings needed for early retirement

While conventional wisdom has it that one can retire and take 7% or more out of a portfolio year after year, this would not have worked very often in the past.^{[7]} ^{[8]} When making periodic inflation-adjusted withdrawals from retirement savings,^{[9]} can make meaningless many assumptions that are based on long term average investment returns.

^{[10]}While the overall market conditions and inflation affected all three about the same (since all three experienced the exact same conditions between 1975 and 2003), the chance of making the funds last for 30 years depended heavily on what happened to the stock market in the first few years.

Those contemplating early retirement will want to know if they have enough to survive possible bear markets such as the one that sent the 1973 retiree back to work after 20 years.

The history of the US stock market shows that one would need to live on about 4% of the initial portfolio per year to ensure that the portfolio is not depleted before the end of the retirement. ^{[11]} This allows for increasing the withdrawals with inflation to maintain a consistent spending ability throughout the retirement, and to continue making withdrawals even in dramatic and prolonged bear markets.^{[12]} (The 4% figure does not assume any pension or change in spending levels throughout the retirement.)

When retiring prior to age 59 1/2, there is a 10% IRS penalty on withdrawals from a retirement plan such as a 401(k) plan or a Traditional IRA. Exceptions apply under certain circumstances. At age 59 and six months, the penalty-free status is achieved and the 10% IRS penalty no longer applies.

### Calculations using actual numbers

Although the 4% initial portfolio withdrawal rate described above can be used as a rough gauge, it is often desirable to use a retirement planning tool that accepts detailed input and can render a result that has more precision. Some of these tools model only the retirement phase of the plan while others can model both the savings or accumulation phase as well as the retirement phase of the plan.

The effects of making inflation-adjusted withdrawals from a given starting portfolio can be modeled with a downloadable spreadsheet ^{[13]} that uses historical stock market data to estimate likely portfolio returns. Another approach is to employ a retirement calculator ^{[14]} that also uses historical stock market modeling, but adds provisions for incorporating pensions, other retirement income, and changes in spending that may occur during the course of the retirement.

## Life after retirement

Retirement might coincide with important life changes; a retired worker might move to a new location, for example a retirement community, thereby having less frequent contact with their previous social context and adopting a new lifestyle. Often retirees volunteer for charities and other community organisations. Tourism is a common marker of retirement and for some becomes a way of life, such as for so called grey nomads.Often retirees are called upon to care for grandchildren and occasionally aged parents. For many it gives them the more time to devote to a hobby or sport such as golf or sailing.

In some countries, retired workers will continue to participate in the life of their family and their society, often following ancient ethnic roles. Some countries are sponsoring initiatives to help retired workers keep contributing to social and cultural life.

Many people in the later years of their lives, due to failing health, require assistance, the highest degree of assistance - in some countries - being provided in a nursing home. Those who need care, but are not in need of constant assistance, may choose to live in a retirement home. This is a facility giving the retired person some degree of freedom, yet with close-by medical assistance to handle emergencies.

Retirement ceases if the retiree decides to go back to work. A retiree may go back to work for a number of reasons, ranging from financial hardship, to the simple desire for activity or new social interactions. New careers where the 'retired' return to work is an increasing phenomenon in Industrialised countries where inflation has reduced the value of available Pension income below that required to maintain a reasonable standard of living. Many corporations are now explicitly recruiting retired workers for their experience, attitude and loyalty.

Old-age pensions are usually not reduced because of other income, so the latter comes on top of the former. This may be different in the case of a disability pension.

## References

- ↑ Normal retirement age (NRA)
- ↑
**Script error** - ↑ Strikes focus on earlier retirement
- ↑ Broverman, Samuel A., Mathematics of Investment and Credit, 3rd. Edition, Section 2.3.1 Actex Publications, Inc, Winsted CT, (2004)
- ↑ A SURE BET? (Wealth Manager)
- ↑ Online Monte Carlo Retirement Planner
- ↑ Getting Going - WSJ.com
- ↑ SC:Lynch #2
- ↑ http://firecalc.com/intro.php volatility
- ↑ FIRECalc: Why another retirement calculator?
- ↑ Dallas Morning News | News for Dallas, Texas | Scott Burns: Columns 2006
- ↑ Retire Early's Safe Withdrawal Rates in Retirement
- ↑ http://retireearlyhomepage.com/re60.html downloadable spreadsheet
- ↑ FIRECalc: A different kind of retirement calculator

## External links

- "Historical Development", Social Security Administration
- "Economic History of Retirement in the U.S.", Eh.net
- Retirement planning calculator, MSN Money
- Retirement calculators
- How Much Will I Need To Save For Retirement Calculator
- "Struggling with retirement",Time magazine
- "Brain Health Roadmap", a joint venture by the CDC and Alzheimer's Association
- "Building the best retirement plan",
*BusinessWeek*, July 19, 1999 - "The Unretired" - HONOLULU Magazine ~ November 2006
- "Boomers Not Saving Adequately for Retirement", "Greater Boston" show with Emily Rooney, WGBH TV, Boston, Massachusetts, aired on August 6, 2007.
- Working past retirement age in the UK
- Retirement Age - Looking at retirement planning options and opportunities for UK residents

Overseas Retirement *- Information for US residents about retiring overseas