I just graduated from college and got a new job that paid me a signing bonus of $$7,500$ and will pay me an annual salary of $$79,000($the median for MIS students, as of the $\text{'}23$ UGA Career Outcomes Survey$).$ The annual salary will be paid in twelve equal monthly installments.

If I put the $$7,500$ signing bonus into my retirement account today and then save $15\%$ of my gross pay every month into that same account, how much will I have saved by the end of my $44$ year working life if I earn $6\mathrm{.}7\%$ APR compounded monthly? Assume I don't get a promotion or increase my contributions throughout the entire term.