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 – zprop ) R repl S {(1+ ireal ) −1+(1+ ireal ) −2 +... ....+ (1+ ireal ) −p} = (1-zprop ) R repl S {(1 – (1+ireal)−p )/ireal} Above is the standard mathematical formula for the sum of a geometric series. (Or if ireal =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 Rrepl=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 ireal=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: zprop S {(1+ i rel to pay )w-1+(1+ i rel to pay )w-2 +... ....+