I think it should be 0.99^10, since you lose 1% every year, just like interest.
Example showing final balance at end of each year:
Year 0: Start with $1000
Year 1: $990 (1% is $10)
Year 2: $980.1 (1% is $9.9)
...
Year 10: $904.38
Example showing final balance at end of each year:
Year 0: Start with $1000
Year 1: $990 (1% is $10)
Year 2: $980.1 (1% is $9.9)
...
Year 10: $904.38