Today is $\frac{1}{7}\frac{?}{2023},$ John plans to deposit $$500$ at the beginning of each month into an investment fund. The first deposit will be deposited today. John predicts that the return

rate of this fund will be $j_2=3\mathrm{.}2\%$ from $\frac{1}{7}\frac{?}{2023}$ to $\frac{30}{9}\frac{?}{2023}$ and $j_2=4\mathrm{.}83\%$ from $\frac{1}{10}\frac{?}{2023}$ to $\frac{31}{12}\frac{?}{2023}.$ What will be the balance amount of this account on

$\frac{31}{12}\frac{?}{2023}?$ Round your answer to three decimal places.

a$.3038\mathrm{.}048$

b$.3038\mathrm{.}404$

c$.3039\mathrm{.}408$

d$.3037\mathrm{.}527$