$1.[15$ Marks$]$ Suppose the annual rate of interest is $\backslash (4\backslash \%\backslash )$ compounded monthly for this question. $($a$)$ Find the accumulated value $\backslash (\backslash$alpha $\backslash )$ of $\backslash (1\backslash )$ received in $1$ month from today? Give your answer to $3$ decimal places. $($b$)$ What is the present value $\backslash (\backslash$beta $\backslash )$ of $\backslash (1\backslash )$ received in $1$ month from today? Give your answer to $3$ decimal places. $($c$)$ Suppose that you would like to buy a car from a car dealer worth $\backslash (15,000\backslash ).$ The dealer gives you a deal for which you pay immediately $\backslash (2000\backslash )$ pounds and then make a payment $\backslash ($ A $\backslash )$ at the end of each month for $5$ years until your debt is paid off with the interest rate mentioned above. Find the amount A you need to pay every month. $($d$)$ Suppose you have invested $\backslash (5000\backslash )$ for $4$ years which produces the following returns: $\backslash (1500\backslash )$ at the end of the second year, $\backslash (4500\backslash )$ at the end of the fourth year, and nothing at the end of the first and third years. What is the internal rate of return of this investment if it is subject to $\backslash (20\backslash \%\backslash )$ capital gains tax payable at the end of the fourth year?