A young couple is saving money in an account to pay for their two$-$year old son's college. They invest an initial lump sum of $$6000$ at $7\%,$ compounded semi$-$annually, and plan to continue contributing $$900$ every $6-$months.

a$)$ How much money will be in the account $16$ years from now?

b$)$ How much money did the couple gain over the term of the investment?