As payouts have shrunk in recent years, with-profits endowments have come under attack for being inflexible and unintelligible. But they still find supporters among financial experts. In a two-page special report, Nic Ccutti explains how they work explains how they work in a two-page special report. Every year millions of people across Britain receive strange letters from their insurance companies, telling them how much their "bonuses" will be. These aren't the huge bounties handed out to City whizzkids but the far more mundane, yet ultimately far more important, sums that are attached to with-profits endowments.

It is on the basis of these annual bonuses, plus a final - "terminal" - payout, made when a policy matures after 10, 15 or 25 years, that many of us hope to pay off our home loans, enjoy a decent income in retirement, or just receive a large lump sum.

The importance of bonus announcements cannot be underestimated. Until recently, more than 60 per cent of mortgage-holders have paid only the interest on their loans. They then made an additional monthly payment in an endowment.

Similarly, over 250,000 people with personal pension policies contribute to with-profits policies. Perhaps 750,000 investors - most of them elderly - have placed billions of pounds into with-profits bonds.

Yet, despite their seeming popularity (even today, 30 per cent of mortgage borrowers still favour them as a means of paying off their loans) endowments have gained a very dubious reputation in recent years. They are attacked as impossible to understand, utterly inflexible and, worst of all, the amounts they pay out are said to be worth less and less - perhaps not even enough to redeem the mortgages they were there to pay off.

Yet they have their defenders, and not simply among the insurance companies which stand to gain from selling them. Amanda Davidson, a partner at Holden Meehan, a highly reputable firm of London independent financial advisers, says: "They may not be suitable for everyone, but I am quite prepared to recommend an endowment to someone. Indeed, I have one myself, along with a personal equity plan (PEP), as a means of paying my own mortgage."

So what exactly is a with-profits endowment? Essentially, it is a vehicle that allows individuals to invest in a range of stocks, shares and property via a life company fund. In most cases, investors pay regular premiums into the fund over varying periods of time, although lump-sum payments into with-profits bonds are also possible.

The investment strategy of with-profit funds is not exceptionally risky - it generally involves between 50 to 60 per cent of a portfolio going into UK equities, some 20 per cent into fixed-interest investments, about 10 to 15 per cent into property, with the remainder placed in overseas stocks.

But unlike traditional equity-linked investments, where the value of a fund rises and falls directly in line with its underlying assets, with- profits funds are different. They involve three separate elements: a guaranteed sum, which pays out at maturity or when the policyholder dies; an annual (or "reversionary") bonus, plus a terminal bonus paid out when the policy matures.

The aim of this labyrinthine bonus system is to "smooth" the peaks and troughs of stock market investment. Once a bonus is attached to a policy it cannot be taken away, locking in value. This means that in the event of a stock market crash, policyholders should not see the value of their fund collapse.

Equally, it means that if markets race ahead, savers may not see all of that upside immediately.