subject : quntitative methods

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$-$Ikhsan College receive some kind of financial aid. Abdul

Rahman Aziz had $3$ years of experience when he went to work in Human Resources at Al$-$

Ikhsan 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$-$Ikhsan 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 faculty members at Al$-$Ikhsan 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$-$Ikhsan College RM$250,000$ per year

for the next $5$ years. Find the present value of these gifts, 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$)$