A payment of $$1,500$ was made into an account at the end of every $3$ months for $12$ years.

a$.$ If the interest rate for the first $4$ years was $6\mathrm{.}00\%$ compounded monthly, calculate the future value at the end of the first $4$ years.

b$.$ If the interest rate for the next $8$ years was $4\mathrm{.}00\%$ compounded annually, calculate the future value at the end of the $12$ year term.