Nationwide has said parents are beginning to get the message about child trust funds (CTFs).
The government initiative is designed to provide all young people with a nest egg for the future and encourage parents to take an interest in saving.
There had been some concern that many of the vouchers sent out by the Treasury had not been used, but Nationwide said this week it had been "overwhelmed" by the demand.
However, Sue Knight, savings spokesperson for the building society, said there was still room for further improvement.
"More needs to be done – there are an awful lot of vouchers that aren't being invested," she said. "There is still more that could be done to encourage parents to make additional payments."
CTFs have been criticised by opposition parties, who claim the initiative is a waste of money.
The Treasury believes they can help fill the savings gap, which has grown in recent years as a result of low interest rates. To read more Investment News, click here.
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