Bradford & Bingley Building Society members will receive shares worth about £1,000 when the society converts to a bank.
But the society has opted for a flat-rate payment scheme, in which all eligible members will receive the same windfall.
The exact payment will depend on the company's value at the time of conversion.
To be eligible, savers must have had at least £100 in their account on April 25 this year, and £100 in the account when the society converts next year.
They must also hold £100 in their account between now and then at a date yet to be specified.
Conversion is still subject to a members' vote next summer.