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 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