2019 Gauss 8 Problem 10

Canadian currency has coins with values \$2.00, \$1.00, \$0.25, \$0.10, and \$0.05. Barry has 12 coins including at least one of each of these coins. What is the smallest total amount of money that Barry could have?

\textbf{(A)}\ \$3.75\quad \textbf{(B)}\ \$3.90\quad \textbf{(C)}\ \$3.70\quad \textbf{(D)}\ \$3.40\quad \textbf{(E)}\ \$3.95

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.