Nathaniel Not perfect but you can also use the balance prediction feature to go back in time. It shows the balance for each day.
Alternatively you can export to CSV format, then open the file in Excel and it should be easy to calculate the account balance for each day through that. If you just need proof for a specific day, you can also export a statement just for that day as PDF, and it will show the account balance, as it always states account balance for the chosen start and end date.