A fund sells Class A shares with a front$-$end load of $2\mathrm{.}5\%$ and Class C shares with $12$b$-1$ fees of $0\mathrm{.}25\%$ annually. The back$-$end load fees start at $5\%$ and fall by $1\%$ each year the investor holds the portfolio until year $5.$ If the annual return net of operating expenses is $10\%,$ what is the value of a $$20,000$ investment in Class A and Class C shares if the shares are sold after $3$ years, which fee structure provides higher net proceeds at the end of the investment horizon? How much is the difference in the net proceeds?

a$)$

Class A; $$44$

b$)$

Class C; $$44$

c$)$

Class A; $$177$

d$)$

Class C; $$177$

e$)$

None of the options are correct.