We must remember that salary increments are given to retain an employee so that he manages the increased cost of living while continuing to work with you. Similarly, a bonus is given for past performance.
Please try to convince your management that you want to pay both increment and bonus for an exiting employee and they will give you the above logic. The concept working with employer brand image in mind exists with very few organizations. Management will tell you that the monies can be used in hiring and training a replacement.
In this particular case, the personal reason is further studies - which is a planned activity. One doesn't decide to do further studies overnight. Once a decision is made, then research into proper institutes, courses, costs etc follows, post which a final decision is made.
So I agree with Ayush - do his appraisal, calculate and release his bonus. It is fair to both employer and employee, which is the line HR should always walk.