I have "solved" this problem by using separate browsers. I use Internet Explorer for the business account and Chrome for my personal account. It is also possible to use "incognito" windows (each with its own set of tabs) for separate accounts. The idea is you need to keep the account information separate. Using different browsers makes it obvious to me whereas it is more difficult to use multiple incognito Chrome windows because they all sort of look the same. However, if you set the group of tabs up appropriately you can keep track of your email, calendar, etc. in that group of tabs as long as you create groups of windows which don't know about each other. That's the whole purpose of the incognito process.