The good news is that many Tessa rates have improved recently, in line with the general edging up of interest rates. Rates are also helped by banks and building societies gearing up to compete for savings that will be freed up by the Halifax and other windfall-yielding societies (see back page).
It is now possible to lock into a fixed rate of 7.5 per cent or more, which is tax-free, of course. And many Tessas whose rates are not fixed at outset but rise and fall in line with interest rates generally (variable rate) are offering 6 per cent or more.
Last week Abbey National launched two league-table topping fixed-rate deals, offering 7.5 per cent a year or, from its Guaranteed Growth Tessa, a total return of 44 per cent after five years. The growth option works out to be slightly more than 7.5 per cent a year but precludes you from taking any income from the Tessa over the five years.
These returns are attractive but also offer the potential to benefit from rising interest rates over the next five years. Any year in which the government base rate is 1 per cent or more than base rate in the previous year, you get a 1 per cent interest bonus for that year.
Both Tessas are open to people with matured Tessas and first-time Tessa investors, but in each case they require you to invest pounds 9,000 on day one. This means that where the rules do not allow all that pounds 9,000 to go immediately into the Tessa, say because you are a first-time Tessa saver and therefore limited to investing pounds 3,000 in year one, Abbey will hold the remainder in a feeder account paying a taxable fixed rate of 7.5 per cent.
The only fixed-rate deal that might appear to beat Abbey's offer is from Clydesdale Bank, in Glasgow, but its 8 per cent interest rate figure is somewhat misleading in that the interest is not annually compounded, so the total return after five years would be 40 per cent (plus a 1 per cent maturity bonus).
There is no definitive answer as to whether it is better to go for a fixed-rate Tessa or one where the interest rate rises and falls, like that on savings accounts generally. Fixed-rate Tessas might be offering more now, but if interest rates were to rise you might be better off with a variable rate.
In theory, if the interest rate on your Tessa starts to look uncompetitive you can transfer to another bank or building society. But transfer penalties are generally so high as to not make this worthwhile. So if you are going to go for a fix, regard yourself as locked in. Transfer penalties on variable- rate Tessas vary, making it important to consider these as well as the headline interest rate when choosing a Tessa.
Another factor that might be worth taking into account when choosing any Tessa is whether you are with a building society that might yield a windfall.
Over the five-year Tessa term there is a good chance that many more building societies will be taken over, giving their savers free cash and shares. This could be worth another pounds 1,000 to Tessa savers.
Our best savings rates table on page 16 gives details of the highest paying accounts with their respective minimum investments. Here are a few other variable-rate deals to consider, that offer a combination of reasonable rates and the possibility of a windfall, and that have minimal impediments for transferring or closing. They are: Coventry building society, 6.65 per cent, seven days' notice (no penalty) for transferring or closing (call 01203 555255); Hanley Economic building society, 6.6 per cent, seven days' notice (no penalty) on transfers or closing (call 01782 208733); Monmouthshire building society, 6.8 per cent, one month's notice to transfer or close (01633 840454). These are all open to first-time Tessa savers and those with Tessas that have matured.
If you close your Tessa (rather than just transfer it) within five years the interest is taxable. But the rates on the three Tessas named above are sufficiently high, and the penalties sufficiently low, to make you better off in these accounts than in a traditional taxable account even if you do have to cash in before five years.
There are also Tessas offering rates that are guaranteed to increase year-on-year, and those whose returns are linked to the performance of the stock market. The key to working out whether "escalator" Tessas (those where the rate rises) are good value is to calculate the average rate over the five years. Generally, you are better off with a straightforward fixed-rate deal.
Do not think, either, that stock market-linked Tessas offer a free lunch - stock market returns with no risk. The price of no risk is that you will not share in the full growth of the stock market. If you want that, go for a PEP.