b$.$ Al$-$Ikhsan College offers students a choice of more than $30$ different majors of study, including business, engineering, hospitality management and information technology. College personnel of Al$-$Ikhsan work closely with students to help them find financial aid. Amazingly, about one$-$half of the students at Al$-$lkhsan College receive some kind of financial aid. Abdul Rahman Aziz had $3$ years of experience when he went to work in Human Resources at AlIkhsan College at a salary of RM$42,000.$ He began work on his $30$th birthday. The college matches his contributions to his retirement plan up to $8\%$ of his salary. Answer the following questions.

i$.$ Abdul Rahman decides to contribute a total of $10\%$ of his salary to his retirement plan. So$,$ American River contributes $8\%$ and he contributes a full $10\%$ of his salary. Find the total annual contribution to the retirement plan.

$(2$ Marks$)$

ii$.$ For planning purposes, Abdul Rahman assumes he will work at Al$-$lkhsan College until he is $60$ and believes he can earn $8\%$ per year in a global stock fund. Assume the contributions continue at the same level as in question $($i$)$ and estimate the future value.

$(2$ Marks$)$

iii. Assume that there are $422$ full$-$time facuty members at Al$-$lkhsan College and that their average income is $$48,500$ per year. Find the annual payroll for the faculty.

$(2$ Marks$)$

iv$.$ Based on the annual payroll in question $($iii$),$ estimate the annual contributions Al$-$Ikhsan College must make into retirement plans if all faculty contribute at least $8\%$ of their salary into their own plans.

$(2$ Marks$)$

v$.$ Assume that a wealthy donor has agreed to give Al$-$khsan. College RM$250,000$ per year for the next $5$ years. Find the present value of these gifls, assuming $6\%$ per year.

$(2$ Marks$)$

vi$.$ Al$-$lkhsan College has decided to build a new classroom building and will need RM$8,250,000$ in $7$ years. They decide to make contributions into a sinking fund at the end of each $6-$month period. Find the payment needed if funds earn $5\%$ per year.

$(2$ Marks$)$

$($Total: $20$ Marks$)$