Check my understanding of this active low-pass filter

As homework (non-assessed) we were given this problem. I worked through it and got a different answer to the textbook, but one that I think is still correct nonetheless. I wanted to verify if my answer was correct by creating this circuit in LTSPICE and playing with the values to see if I could predict the output. I'm pretty close to the simulated result but there is a slight difference and i'm not sure if that's because my working is out or if that's just the natural limitations of simulations.

Here's the circuit i'm using for this example. Here is how I worked through it. My answer is pretty close to what the simulation gives (it's about 0.8% off). I'm not 100% sure on that step where I found the magnitude of the impedance (i.e. this step here). I did this based on intuition, I don't recall learning this in a lecture/tutorial.

Edit: here's a picture of the simulation output