The purchase date isn't the important info here. The actual model of the iMac is and this info is in the model identifier. For example, I have a late-2012 iMac, model identifier is iMac 13,2. I will add that there is no 2013 model available. The most recent at this time is the late-2012 model which I have.
On my display if I select Apple->System Preferences->Displays then press the button "Display" I am presented with a screen which shows Resolution and Scaled as button options. "Best for built-in display" is the default, however, clicking on "Scaled" brings up the various resolutions that can be used with the display:
From this I can select a display with larger items, but keep in mind that while a larger image can be selected (using a smaller width x height value) it will not be as crisp and sharp as the default.