a$)$ Calculate the value at the end of the tenth year of $100$ invested at an annual rate of interest of $12\%.$

b$)$ Calculate the value at the end of the third year of $300$ invested at an annual rate of $5\%.$

c$)$ Calculate the value at the end of the fifth year of $500$ invested at an annual rate of $12\%$ compounded monthly. What is the effective annual rate in this case?

d$)$ Calculate the value at the end of the fourth year of $500$ invested at a nominal rate of $12\%$ compounded quarterly. Calculate the effective annual rate.

e$)$ What is the effective annual rate equivalent to an interest rate of $15\%$ payable four times per year?