Police believe someone may be holding back
Surrey Police hope the reward - offered by The Sun - will prompt people to come forward with vital clues to the 13-year-old's disappearance.
Amanda, known as Milly, vanished six weeks ago on her journey from school to her home in Walton-on-Thames, Surrey.
Superintendent Alan Sharp said: "We have spoken to many people but we believe they may be holding something back about Milly.
"There may be secrets about Milly or her life - we need to know what these secrets are."
Chief Constable Denis O'Connor said: "We think that there is someone out there who knows something that they are not telling us.
"We sincerely hope that this fresh approach will spark someone to tell us any secrets about Milly that they know."
The Sun's editor David Yelland said: "Somebody knows where Milly is and we hope this reward will persuade them to call Surrey Police with that vital piece of information.
"We want to do anything we can to help bring Milly back to where she belongs with her parents."
Police believe Amanda's school friends may hold a clue about her disappearance.
On Friday officers visited fellow pupils asking them to tell of any secrets she may have told them.
Mr Hollingsworth told pupils: "We want to know about your private thoughts and conversations with Amanda.
"These might be conversations in or out of school, over internet chatrooms, or text messages.
"We need to know any secrets that various friends and groups keep. We need to know everything."
He reminded pupils of the unconfirmed sightings of Amanda the day she went missing on 21 March.
These sightings include reports of a girl seen in Walton talking to a man near a car, a girl seen near a transit van and also a schoolgirl seen crying.
Purse ruled out
He said officers would be interviewing new witnesses and re-interviewing people.
Mr Sharp told BBC News: "Friends of Amanda have been extremely helpful and honest but there still maybe something that for whatever reason, they have been withholding."
Surrey Police said later that a purse found in the hunt for Amanda did not belong to the teenager.
The purse found by a woman in Walton-on-Thames was said to be similar to the white purse with a red heart that Amanda was carrying when she vanished.
It was shown to her family a few weeks ago but they said they did not think it was hers, and police said forensic tests had later confirmed that.
It was the second similar purse, from Clare's Accessories, to be given to detectives.