Look into Mint.com. There is an app for iOS and you can also access account information via a web browser on your PC. I don't know if there is a limit on the number of accounts, and if so, what it is, but it is set up to monitor multiple accounts from multiple institutions.
Another vote for Mint - great app. I access my account from iPhone/iPad using their app and any computer using a browser. The budgeting features work really well. You should be able to sync all 15 accounts, assuming Mint supports all those accounts.