multilevel random effects model

I want to look at the change in the percentage of income savings measured in dollars using repeated measures data for older adults. I want to compare three groups based on their father's occupation while growing up.

I want to estimate different slopes and intercepts for the three groups. For example: group A is subjects whose father's were blue-collar; group B is subjects whose father's were white-collar; group C is subjects whose father's were other types of workers. I have repeated measures for 10 annual surveys and subjects reported how much of their income they saved. I want to see if the intercept and trajectory differs for the three groups.

This is what I come up with but I am not sure if this gets at the appropriate verbal explanation. Thank you very much for your time. I truly appreciate it. Thank you!

m1 = xtmixed savings time || subjects:, var m1 looks at the impact of time on savings and estimates intercepts and slopes for each subject.

m2 = xtmixed savings time##fathers_occupation || subjects:, var Does m2 examine the differences in the intercept and slope for the two groups? Or do i need to add fathers_occupation to the right side of || as well?