1. The problem states that Samuel initially has $415 in his bank account and deposits an additional $135. 2. To find the new account balance, we need to add the initial amount and the deposit. 3. The formula for the new balance is: $$\text{New Balance} = \text{Initial Balance} + \text{Deposit}$$ 4. Substitute the given values: $$\text{New Balance} = 415 + 135$$ 5. Perform the addition: $$415 + 135 = 550$$ 6. Therefore, the integer that represents the new account balance is $550$.