For the last ten years Joe has made deposits of $$550$ at the

beginning of every month earning interest at $6\%$ compounded

quarterly. He leaves the accumulated balance for another five

years at $4\%$ compounded semi$-$annually.

a$)$ What will the balance be in Joe's account at the end of the

fifteen$-$year period?

b$)$ How much did Joe contribute?

c$)$ How much will be interest?