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Cash ISAs, the new tax-free savings schemes masterminded by Geoffrey Robinson, the controversial former Paymaster-General, are proving an instant hit with savers with lump sums to invest, leaving Tessas, the accounts that they replaced, in the shade; however, they are failing to attract the small savers with just a few pounds to put away.

Providers of ISAs - Individual Savings Accounts - are reporting that anywhere from three times to 20 times as many cash ISA accounts have been opened in the past month as Tessa accounts were opened in the same period a year ago.

The most common explanation put forward for these phenomenal sales figures is that ISA sales have been boosted by the sheer amount of hype surrounding the launch of the new savings plans in April.

Alan Samuels, the general manager (business development) at Norwich & Peterborough Building Society - which is offering the highest-paying ISA on the market at 6.75 per cent for a minimum investment of pounds 1,000 - says: "We're getting a lot of people who are buying from the `Best Buy' tables. There's no doubt at all that a lot of people are driven by the rates".

Cash ISAs are also offering better returns than Tessas, the investments that they replaced. Tessas, as The Independent warned last year, are in danger of becoming "obsolete" accounts, in which savers find themselves trapped by the prospect of losing all their tax advantages if they decide that they want to pull their cash out of the account.

The Nationwide Building Society, for example - which, of all the national institutions, is currently the best buy for small savers - is paying 6.5 per cent on anything from pounds 1 upwards in a cash ISA against 5.85 per cent on a Tessa, and wider differentials are increasingly common elsewhere.

However, ISAs are, in turn, failing to attract the small savers in the amounts that the Government hoped that the new savings accounts would, if the first-month sales of the new plans are an accurate measure of overall demand.

Figures from leading ISA providers show that even cash-only plans or cash mini-ISAs, which are likely to hold maximum appeal for small savers, are pulling in average deposits of over pounds 2,000 per plan. As the maximum investment is pounds 3,000 in the current year, it means that relatively few regular savings plans have been opened so far.

Judith Cork, who is Halifax's head of savings, has been studying the situation. "They are certainly not attracting the smaller sums," she says. "We're not talking about pounds 50 or pounds 100 - it's in the thousands."

Another senior savings executive, who asked not to be named, echoes her findings, declaring: "The Government's pie-in-the-sky fantasy that ISAs were going to have an appeal for the small saver was, quite frankly, rubbish. The big market for ISAs was always going to be those people who had invested their money into Tessas and PEPs, and that's been borne out by the results."

We will know more when the Inland Revenue releases its own first set of ISA take-up statistics in September or in October. However, the early sales figures already paint a consistent picture of the appeal of ISAs. Lloyds TSB, for example, says that its average deposit in a cash mini- ISA stands at pounds 2,300, while Norwich & Peterborough puts its own figure at pounds 2,800. NatWest has taken an average deposit of pounds 1,600. Barclays will not give a figure, but it admits that its average deposit is skewed towards the top end of the cash ISA's maximum investment of pounds 3,000.

Many providers are setting minimum investments of pounds 1,000 or more and specifically excluding small savers, while others pay better rates on larger sums. Nationwide is currently the best buy for small savers but is unwilling to reveal the response to date. National Savings is specifically targeting small savers, but its standard rate of 5.75 per cent has been outbid by other providers.

The Co-op is running a pilot scheme aimed at very small savers in its Scottish stores. The Co-op spokesman, Dave Smith, says: "In Scotland, people are taking up the option of being able to pay in at the till. It's people putting small amounts of savings in, and that's what cash ISAs are all about. I don't think the people we're aiming our cash ISAs at are going to be putting a spare thousand pounds in." But the Co-op only offers 5.5 per cent, and Mr Smith will not give a figure for the Co-op's own average cash ISA deposit, claiming the information is commercially sensitive.

Judith Cork thinks many very small savers may have been put off buying an ISA because they believe - wrongly - that ISAs lock your money away in the same way that Tessas do. She says: "One thing we're finding from our branch network is that customers still feel they would be locked in with a cash ISA. It's a shame, really because they are genuinely instant access accounts."

But rushing into a cash-only mini-ISA without thinking the wider issues through could be disastrous for people who also hope to put some ISA money into shares. Once you have bought a mini-ISA - however small - that rules out having a maxi-ISA for the whole year. The biggest amount you can put into shares via a maxi-ISA in the current tax year is pounds 7,000. But the most a mini-ISA will let you put into shares is just pounds 3,000.