I might be splitting hairs, but the British English word "institute" is a verb - not a noun. This view is supported by my copy of Collins Dictionary, although not by the Concise Oxford Dictionary. Nevertheless, I think the British English word "institution" should be accepted as a correct answer.
Are there any other views out there?
They all give a definition along the lines of:
- an organization founded for particular work, such as education, promotion of the arts, or scientific research
- the building where such an organization is situated
- something instituted, esp a rule, custom, or precedent
The other contributors are right by saying that it should be 'institution' rather than 'institute', but not for the reason given. You are right that 'institute' is a noun! However, the word 'institution' covers a wide variety of organisations which includes places of learning. The word 'institute' has a much more limited meaning (in British terms) and it is unlikely that you would study there. You give a the names of a number of learned British 'institutes', but these are professional societies and not places where a person would study. Historically ,'Mechanics Institutes' offered courses of education but that was in the nineteenth century.
I was hoping to find some comments on the difference between "institute" and "institution" but didn't expect a raging war zone! I do think that in the context of this sentence, which is about studying, "institution" is the more likely option, as it suggests a school, college or university. At least, in South African English.