James invests $$15,000$ in a $5-$year Guaranteed Investment Certificate $($GIC$)$ with a variable interest rate that changes annually. The interest rate for the first year is $5\%,$ and it increases by $1\%$ each subsequent year. Interest is compounded quarterly. Calculate the following:

a$)$ The Maturity Value of the GIC after $5$ years.

b$)$ The Annual Rate of Return $($Effective Annual Rate, EAR$)$ for the GIC.

c$)$ If James decides to withdraw the GIC after $3$ years, calculate the amount he would receive, and determine the Annual Rate of Return for the period he held the GIC.