I am not guaranteeing this is correct:

If [Period] < 5 Then [AdContractPrice] = [AdultFare] * 31.5
If [Period] > 4 and If [Period] < 7 Then [AdContractPrice] = [AdultFare] *
[Period] * 7.65625
If [Period] > 6 and If [Period] < 10 Then [AdContractPrice] = [AdultFare] *
[Period] * 7
If [Period] > 9 Then [AdContractPrice] = [AdultFare] * [Period] * 6.5625

I will assume that Period is a whole number.  Scubadiver is on the right
track, but the If doesn't appear twice.  Also, I would use the Me syntax:
If Me.Period > 4 and Me.Period < 7 Then ...

Select Case may be simpler to write:

Select Case Me.Period
   Case < 5
       Me.AdContractPrice = Me.AdultFare * 31.5
   Case < 7
       Me.AdContractPrice = Me.AdultFare * Me.Period * 7.65625
   Case < 10
       Me.AdContractPrice = Me.AdultFare * Me.Period * 7
   Case Else
       Me.AdContractPrice = Me.AdultFare * Me.Period * 6.5625
End Select

As soon as a condition is met, Select Case ends.  If Period is 6 it is not
less than 5, but it is less than 7, so the second case applies.  No more
conditions are tested.

Using If statements as you have done (sequential rather than being nested),
it *is* necessary to check the > and < values each time, since each
condition will be tested every time the code runs.  By the way, you can use