Human lifespan has increased enormously this century. But we remain uncertain about the forces that reduce mortality, and about the cost implications of ageing populations and their associated social burden. The poor understanding of the factors driving mortality decline, and the difficulty of forecasting mortality are due in part to the pronounced irregularity of annual to decadal mortality change. Here we examine mortality over five decades in the G7 countries (Canada, France, Germany, Italy, Japan, UK, US). In every country over this period, mortality at each age has declined exponentially at a roughly constant rate. This trend places a constraint on any theory of society-driven mortality decline, and provides a basis for stochastic mortality forecasting. We find that median forecasts of life expectancy are substantially larger than in existing official forecasts. In terms of the costs of ageing, we forecast values of the dependency ratio (that is, the ratio of people over 65 to working people) in 2050 that are between 6% (UK) and 40% (Japan) higher than official forecasts.