Instagram is close to releasing an update for their Android and iOS apps that will allow support for multiple accounts. This is great news for those that manage personal and business accounts. You will no longer need to log out and back in.
There is a beta available for Android users and iOS users will need to wait for the update to release. Users will be able to switch accounts by tapping on the user name at the top of the app. There will be a drop down selection available to change accounts.