Today is $1/7/2021,$ 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 $j_2=5\mathrm{.}42\%$ from $1/7\frac{?}{2021}$ to $30/09/2021$ and $j_2=3\mathrm{.}62\%$ from $1/10/2021$ to $\frac{31}{12}\frac{?}{2021}.$ What will be balance amount of this account on $31/12/2021?$ Round your answer to three decimal places.

a$.3035\mathrm{.}554$

b$.3036\mathrm{.}075$

c$.3036\mathrm{.}398$

d$.3037\mathrm{.}435$