$($a$)$ Daniel wants to be able to withdraw RM$8,000$ at the end of four years and withdraw$$ RM$10,000$ at the end of seven years, leaving a zero balance in the account after the last$$ withdrawal. If he can earn $6$ percent on his balances, calculate how much Daniel needs to deposit today to satisfy his withdrawal needs.$(6$ marks$)$

$($b$)$ Brian just graduated from university. He was fortunate to earn money from freelance work$$ he did during his studies over the past four years. His earnings were as follows:$$

Year$$ Pay

$1-$ RM $15,000$

$2-$ RM $14,500$

$3-$ RM $16,200$

$4-$ RM $15,800$

He has saved the money in a fixed deposit account that pays $5\mathrm{.}5$ percent interest$$ compounded quarterly. Calculate Brian$$s account balance after the last deposit. $(6$ marks$)$