Commencing January $12023$ Hayley plans to deposit $$500$ at the beginning of each month into an investment fund. The first deposit will be made on January $12023.$ Hayley predicts that the rate of return on this fund will be j$12=5\mathrm{.}48\%$ p$.$a$.$ from $1$ January $2023$ to $30$ June $2023$ and j$12=4\mathrm{.}04\%$ p$.$a$.$ from $1$ July $2023$ to $31$ December $2023.$

If we assume these deposits are made at regular intervals, what will the balance of this account be on $31$ December $2023?$ The correct answer is: $6145\mathrm{.}96$