Editing Retirement (section)

===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.