The online survey of more than 1000 teenagers - most still at school or in further education - also says 41 per cent of those questioned believed their parents would be financially worse off if Scotland said Yes compared with one-fifth who thought their parents would be better off.
For the first time in a major vote in the UK, a younger age group will be allowed to participate and is regarded by both sides in the referendum debate as an important constituency.
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Earlier this month, official statistics showed more than 98,000 16 and 17-year-olds, representing about 80 per cent of the total in Scotland, had already registered to vote for the referendum with the deadline for registration still some time off on September 2.
The opinion poll, which also targeted 15-year-olds who will be 16 and eligible to vote in September's referendum, was undertaken around the turn of the month by Carrington Dean, a Glasgow-based firm of independent financial advisers. It found:
l 64 per cent of 16 and 17-year-olds worry about the economic outlook in an independent Scotland, 17 per cent do not, while six per cent say independence would have no economic impact;
l 41 per cent believe their parents would be financially worse off in independent Scotland, 21 per cent think they would be better off, and 18 per cent say there would be no difference;
l 39 per cent think their own generation would be financially worse off in an independent Scotland, 25 per cent think they would be better off, and 22 per cent say there would be no difference;
l 69 per cent say an independent Scotland should keep the pound, 12 per cent say it should have its own currency and six per cent it should adopt the euro.
Carys Hughes, a Better Together youth representative, said: "Alex Salmond may want us all to think smaller, but it's clear from this survey that we've got a message for him: we are not going to."
Sarah-Jane Walls, a spokeswoman for Yes Scotland, said: "We are confident as more and more young people engage in the debate they will see through the shallow negativity of the No campaign and seek real information about what independence will mean to them."
She added: "The more people find out about the gains to be had with a Yes, the more they realise that Scotland can, and should, be a fairer and more successful independent country with the benefits shared by all - young and old."
Peter Dean, managing director of Carrington Dean, said its survey showed teenagers were engaged on critical issues for the nation. "They are reaching maturity at a time when many families are struggling with debt and the problems it causes for families. It will be interesting to see how these financial concerns play out when they enter the polling booths in September."
Elsewhere, a more general snapshot suggested English voters living in Scotland could swing the independence referendum towards a No vote.
Some 66 per cent of English people living in Scotland said they intended to vote No, compared with 42 per cent of Scots, a Panelbase poll found.
Independence was the most popular choice among Scots, with 44 per cent intending to vote Yes compared with just 27 per cent of English people. But the weight of non-Scottish votes was enough to sway the vote towards No, with overall support for keeping the UK at 47 per cent compared with 40 per cent for Yes. Meantime, a separate ICM poll placed support for independence at its lowest point since last September. Only 34 per cent of people supported independence, down five points since the last ICM poll in April. Support for the UK was up four points from last month to 46 per cent.
Blair MacDougall, the Better Together campaign director, said: "When even the SNP's favourite polling company Panelbase is showing the Nationalists going backwards, then you know they are in trouble."
But Yes Scotland's Blair Jenkins said: "With precisely four months until the independence referendum, it is all to play for. The Yes movement has made big gains over the last six months and we are confident the upward trajectory of Yes will continue through to September."
At the weekend, the Queen sent a letter to the General Assembly of the Church of Scotland praying for both sides in the debate to work together for the social good of Scotland whatever the result, signalling the monarch's concern at the potential divisive consequences of the referendum.