The sum is based on calculations from City regulator the Financial Services Authority (FSA). It represents the average cash expected to be lost in retirement by older savers who contribute regularly to a personal pension and who have "contracted out" of their entitlement to the state second pension, or S2P (formerly Serps).
While £3.90 a week doesn't sound much, it adds up to £202.80 a year for every year of retirement. As the vast majority of Britons live to a ripe old age, this means thousands of pounds are at stake for each person affected.
S2P is based on your earnings and is intended to shore up your basic state pension. If you are saving towards a personal pension, you currently have a choice each year: let the government keep S2P and work out your entitlement when you retire, or "contract out". Take the latter route, and you will receive a rebate to invest in a fund that will grow alongside your other savings.
If you're saving through a company pension - either a final-salary or a regular money-purchase scheme - you won't usually need to make decisions about S2P. They'll be taken for you by the pension fund trustees.
The hoopla caused by the publication of the FSA's research last week reflects the serious implications for the millions of savers who have contracted out via personal pensions.
A combination of dwindling government rebates and falls in the stock market has led to unimpressive returns on contracted-out investments.
The practice of contracting out began in earnest in 1988, at a time when the Thatcher government was looking at ways to reduce the burden of the state pension. A one-off bonus of 2 per cent of salary was offered as an incentive, and millions were persuaded to make the change.
The FSA's £3.90 a week is the sum it calculates will be lost by those who have remained contracted out from 1988 to the present day. Those who stayed out for any five-year spell between 1988 and 2004 will be about £2.03 a week worse off, the FSA found.
Savers who were advised to contract out by either their independent financial adviser (IFA) or a tied adviser working for a pension provider could have a case for mis-selling, the FSA has implied. It is now talking to a small number of providers and IFAs about their contracting-out advisory processes.
The consumer body Which? has found that an estimated 4.5 million people who took themselves out of the state scheme are likely to get less than if they had stayed in. Those who contracted out, or stayed out, after 1997 are the "really big losers", it says.
From this year, the S2P rebate became age related: the younger you are, the less rebate you'll get in your personal pension pot.
"Given the Government's stated concern over the pension 'savings' gap, it's time it gave us some clear direction on opting out, before millions lose out [any further]," says Teresa Fritz of Which?.
Unfortunately, the Government isn't offering much. "We provide leaflets on contracting out but, ultimately, it's up to individuals themselves to decide what form of provision is best for them," says a spokeswoman at the Department for Work and Pensions.
Some insurers, including Norwich Union and Prudential, have - after consultation - contracted older policyholders back in.
But reaching a decision is far from easy. Many of the same tied advisers who merrily sold, for commission, the "contracting-out" plans in the late 1980s and early 1990s have either gone out of business or no longer advise on such matters.
As a general rule, says Patrick Connolly of IFA John Scott & Partners, you're probably better off staying contracted in if you're much older than 50.
"At that age, you won't have enough time to build up contributions," he explains. "But if you're younger, it's a grey area."
If you're 30 and contracted out, at least you'll get some cash in a pension pot with your name on it.
But as Mr Connolly concludes: "The problem is that nobody knows the right answer. The state pension might not be here in 30 years."
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