I thought the thing about a fractional reserve system was that the currency can be increased by 90% each time bringing git to a total of about 80x every dollar invested or something (I don't have the accurate figures).
I'm trying to figure out what it is that you mean when you ask where the inflated money "goes". Every dollar still exists, the difference is that it is worth less individually because of the constant re-issue of it in the form of debt. The original dollars aren't going anywhere.
You're pretty close with your comment that each dollar can create an additional 80, because they can re-issue up to 90% of a deposit a ridiculously large amount of times, if not every time it's deposited.
If you're trying to ask where the money goes once it's paid back, it turns into a profit for the bank. Inflated money just kind of continues to exist once it's "repaid", although the debt can never be truly paid back because there is always more money required to pay back the interest as well as the principle than that which existed in the first place.