Nearly 20 per cent of people alive today in the UK will reach their 100th birthday, the Department of Work and Pensions has calculated.  The claim  attracted quite a few headlines, and Pensions Minister Steve Webb called the figures “staggering”.
 
Only so if you hadn’t read the ONS National Population Projections, published in 2009, which made estimates of the future population by age band through to 2081. By then, ONS said, there will be 651,000 people over the age of 100 out of a total UK population of 85 million. The DWP’s figure for 2080 is 626,000, so actually the new estimates are slightly less staggering than the older ones.
 
Since everybody who will be more than 100 in 2081 is already alive, it’s easy to see that if these projections are right, a lot of people alive today are going to make it to 100. The DWP estimates that 17 per cent will – more than ten million people.
 
However, it’s easy from this to jump to the false conclusion that the UK will by 2081 have millions of centenarians alive at the same time. As the figures show, the numbers alive in any particular year, though high, are more modest.
 
Today there are about 12,000 centenarians in the UK. By 2030 that will have risen to 59,000, by 2041 to 155,000, by 2051 to 281,000 and by 2061 to 399,000 (ONS estimates; the DWP ones are very similar.)
 
That growth rate means that by 2066 there will be roughly as many people over 100 (507,000) as there are today over 90 (467,000). Go back to 1971, and there were just about the same number (484,523) over 85. So tomorrow’s 100 is today’s 90, and yesterday’s 85.
 
Is that an issue to worry about? It depends, of course, on whether living longer means more years of health, or more of dependency. It has implications for pension provision and without changes in pension ages the dependency ratio – the numbers of pensionable age per 1,000 of working age - would rise from around 310 today to 376 by 2021 and 495 by 2051.
 
The changes already planned – raising women’s pension age to 65 and later both men and women’s to 68 – will be sufficient to produce a dependency ratio of 343 by 2051 – not hugely different to today’s.
 
All the projections are based on some heroic assumptions, the principal one being that mortality rates will continue to decline by about 1 per cent a year. Is there a limit? In 2008, mortality rates among over-85s in the US actually increased by 0.6 per cent, with the majority white non-Hispanic population driving the change. This is probably a one-year blip, linked to the recession.
 
It’s also striking that although more people are surviving to be 100, the oldest age anybody ever achieves does not seem to be changing much. A few survive to 110 and beyond, but not to 120 or 130.
 
Since 1955, the verified age of the oldest person in the world has changed little, settling at around 114-116. While there are 11,800 people in the UK today over 100, there are fewer than 100 over 110.
 
Not everybody believes the statisticians. The bookmakers William Hill were quoted by the BBC as happy to offer 100 to one on any newborn baby reaching 100, and 50 to one on any 50 year-old. This is based on the practice of deducting your age from 100 to work out the odds.
 
Since the DWP estimates that a quarter of today’s newborns will reach 100, and 10.8 per cent of 50 year-olds, those are generous odds. But at 100, would you care? And would William Hill still be around to collect your winnings from? The odds on a 95 year-old reaching 100, at 5 to one, are actually remarkably close to the figures quoted by the DWP, which suggest that just under one in six 95 year-olds will reach this goal. .