Numerical Test Help, Simple Question

Hi guys, could you help with a simple numerical test question (below)

-----given chart/information-----

Annual number of non-fatal major injuries at work:
Rate (per 100.000 employees) in Services sector:

5 years ago: 57.5
Now: 51.3

-----question-----

Over the next 5 years, safety in the Services sector is expected to improve by only half the rate it has shown over the past 5 years. What will be expected major injury rate, per 100.000 employees, 5 years from now?

A 43.3
B 45.1
C 45.8
D 48.2
E 48.5

I understand that one could easily write:
51.3-(57.5-51.3)/2
and get (D) 48.2, but is that a correct answer?

Since they are talking about rates, would this be more appropriate solution:
((51.3/57.5-1)/2-1)*51.3
so the answer would be (E) 48.5 (48.53 to be exact, but rounding is allowed)

Thanks!