Being preoccupied with your retirement income, you start planning to save money for retirement over the next $20$ years. You plan to invest in two investment vehicles: stocks and bonds. You will thus invest $$600$ a month in the stock account and $$300$ a month in the bond account $($your monthly investment would thus be used to purchase stocks and bonds for $$600$ and $$300$ respectively$).$ The stock account is expected earn $12\%$ per year $($corresponding to a monthly rate of $12\frac{\%}{12}$ per month$),$ and the bond account is expected to earn $8\%$ per year $($corresponding to a monthly rate of $8\frac{\%}{12}$ per month$).$ When you retire, you will combine your money into an account with a $6$ percent return per year $($corresponding to a monthly rate of $6\frac{\%}{12}$ per month$).$

a$)$ What is the value of the stock account $20$ years from now? $(6$ Marks$)$

b$)$ What is the value of the bond account $20$ years from now? $(6$ Marks$)$

c$)$ What is value of the combined stock and bond accounts $20$ years from now? $(7$ Marks$)$

d$)$ How much can you withdraw each month from your account after retirement assuming a $25-$year withdrawal. $(6$ Marks$)$