The welfare state, not just in the UK but throughout the developed world, is under huge pressure. The reason is not politics but arithmetic.

The key to the success of what is often called “national insurance” is that each generation of working people supports the previous generation once they have retired. When populations were rising and people died at a relatively young age, this system worked very well. The system was designed when there were roughly four workers for every retiree. Ageing societies now mean there are between two and three workers for every retired person; as longevity increases, the ratio will fall below that. In the case of Italy, it has been projected there will soon be little more than one worker for every pensioner.

So what’s to be done? Increased longevity is wonderful. It’s a tribute to improved housing and healthcare, and in some measure is a result of the success of western welfare systems. Governments are chipping away at the problem by increasing retirement ages and pension contributions of working people, but the numbers are inexorably against them. In any case, there is political pushback against younger, poorer people being made to support older and, in some nations, wealthier generations. Tension between young and old is one of the most troubling forces in most western democracies. The smaller cohorts of the young have to pay the money, while the larger numbers of the old have the voting power.

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No one can know what the political climate will be in, say, 30 years’ time, but younger people in work now cannot assume that the present level of benefits will be maintained. The balance of probability is that they won’t.

If, then, you look at this from a personal perspective, rather than a political one, the only sensible thing for young people to do is to make their own provision for pensions and healthcare. In short, to assume the state may no longer be there to help.

That sounds harsh, but it is prudent because we cannot judge what policies voters will support in 2050 and beyond.

Fortunately the mathematics that are undermining state support work in the opposite direction for personal support. The key is for people to save, and the magic words are “compound interest”.

Over the past 150 years – and for any 40-year period within that – the real return on equities in almost every developed country has been between 5 and 7 per cent. Of course the next 150 years may be different. The yield on bonds is lower now in just about every country than at any stage in the past 150 years. In fact, interest rates in Europe are lower now than they have ever been – with the possible exception of the period after the Black Death in the early 1350s, when one-third of Europe’s population died.

But – and this is the key message – there is a strong probability that a reasonable spread of investments will yield an average 5 per cent return over the next 30, 40 or 50 years. That is where compound interest kicks in.

The maths are very simple: assume someone starts with £1,000 and adds to that pot another £1,000 every year. At 5 per cent the pot in 40 years’ time will be worth £133,880.

You can play around with the numbers, but it should be possible for anyone on UK average earnings to amass a pot of about £1m (in present day values) over 40 years. If that sounds absurdly high, consider this: the median wealth of a British family is now £240,000. That is the median – the middle family in the land – not the average, which is higher because it is skewed up by the very wealthy.

The question is, how can people be persuaded that such a path is attainable, particularly since the financial services industry has such a bad reputation? Here I think several things have to happen, starting with financial services. It has to clean up its act, cut its fees and get rid of the crooks. Auto-enrolment of pensions is a useful nudge, but the government could surely do more. Not chopping and changing pension legislation would be a start.

But I think the core of it is education: teaching everyone – starting with children – about the mathematics of finance. How to do that will be a huge challenge, but at least we know what we need to do.

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