Starting on the day Brian was born, his mother has invested $$30$ at the beginning of every month in a savings account that earns $3\mathrm{.}20\%$ compounded monthly.

a$.$ How much did Brian have in this account on his $18$th birthday? Assume that there was no deposit on that day.

Round to the nearest cent

b$.$ What was his mother's total investment?

Round to the nearest cent

c$.$ How much interest did the investment earn?