Is it ‘you’ or ‘your’?

I HOPE you can guide me on the use of “appreciate”, which seems to be quite popularly used in business letters nowadays.

I have conflicting views between what I learned at school and what is used in business letter-writing. It concerns the use of “you” and “your” after “appreciate”.

For example:

We appreciate you taking the time to complete our feedback form.

OR

We appreciate your taking the time to complete our feedback form.

The conflicting examples show the difference between the formal use of a possessive before a gerund (“your making”) as opposed to the informal use of the object form of a pronoun before a gerund (“you letting us know”). These uses can be found not just after the word “appreciate”.

If you are writing a business letter, it would be better to use the formal style of writing. The following is the reasoning behind the use of a possessive form like “your” before a gerund:

Take, for example, the sentence you gave me, i.e. “We appreciate your taking the time to complete our feedback form.” In that sentence, “taking” is a gerund, an ‘-ing’ verb which is treated like a noun. A noun is qualified by “your” rather than “you”. If I substitute “taking the time” with a noun like “help”, I would have to write “We appreciate your help ...”, NOT “We appreciate you help...”.