The problem is within the add_interest function:

def add_interest(balance, rate):
    balance += balance * rate / 100

This creates a new float object, balance, local to the function, which is independent of the original balance object. When the function exits, the local balance is destroyed and the original balance never updated. One fix would be to return the updated balance value from the function:

>>> balance = 100
>>> def add_interest(balance, rate):
...     balance += balance * rate / 100
...     return balance
...
>>> for year in range(4):
...     balance = add_interest(balance, 5)
...     print('Balance after year {}: ${:.2f}'.format(year+1, balance))
...
Balance after year 1: $105.00
Balance after year 2: $110.25
Balance after year 3: $115.76
Balance after year 4: $121.55