You are about to begin regular month$-$end contributions of $$350$ to a retirement fund. The fund's long$-$term rate of return is expected to be $3\mathrm{.}5\%$ compounded semiannually. Rounded to the next higher month, how long will it take you to accumulate $$500,000?$

Group of answer choices

$48$ years and $1$ month

$48$ years and $2$ months

$48$ years and $4$ months

$47$ years and $2$ months

$47$ years and $6$ months