Charitable organisation Grand Central Savings aims to reward careful savers, who do not need an address, by awarding a bonus after one year - with strict limits and conditions to avoid misuse. The charity is also preparing for an expansion from its roots in Glasgow across Scotland, starting with Aberdeen.
Founded to address financial problems faced by homeless people, it has recently opened to the wider public facing tough economic times brought on by the recession.
Chief executive Jackie Cropper said: "We have successfully opened another branch in Greenock and we're working towards opening a branch in Aberdeen next year.
"Because of the recession, Grand Central Savings has found a lot more people coming forward. More people are finding themselves bankrupt and need support."
The scheme was previously held up through a lack of funding. It would allow customers to bank up to 10 a month over one year, with a savings bonus of 50 per cent at the end - a potential extra 60 on top of the maximum 120 saved.
The charity said a philanthropic trust gave enough money to open the scheme to a "minimum of 500" customers in Glasgow and Inverclyde.
Further details of the plan are expected to be unveiled in the new year before its official launch.
Grand Central Savings was established in 2001 in Glasgow, originally as part of the Big Issue Foundation Scotland, but has operated as an independent charity since 2008.
About 2,600 customers have savings accounts with the charity. Since the launch, about 19 million has been distributed.