$($a$)$ RM$75,000$ is placed in a fixed deposit account with an interest rate of $4\mathrm{.}5\%$ p$.$a$.$ The fixed deposit pays interest every half year with roll$-$over interest. Compute the money available after $10$ years. $($b$)$ David requires RM$80,000$ in $5$ years$$ time. He has placed his funds in a vehicle that generates an annual compounded rate of $7\mathrm{.}75\%.$ How much must he invest in a lump sum now? $($c$)$ Assume that you plan to buy a condominium $5$ years from now, and you estimate that you can save RM$2,500$ per year. You plan to deposit the money into the bank that pays $4\%$ interest, and you will make the first deposit at the beginning of each year. How much will you have after $5$ years? $($d$)$ There are $2$ investment plans, X and Y$.$ Plan X involves setting aside RM$500$ at the beginning of every quarter for $10$ years. Plan Y requires an amount of RM $250$ at the beginning of each quarter for $20$ years. If the rate of return is $9\%$ a year compounded quarterly, which plan provides a higher future value?