Question $4$

A father is planning a savings program to put his daughter through university. His daughter is now

$13-$year$-$old. She plans to enroll at the university in $5$ years, and it should take her $4$ years to

complete her education. Currently, the cost per year $($for everything $-$ her food, clothing, tuition,

books, transportation, and so forth$)$ is GH$12,000$ per year. This cost is expected to remain

constant throughout the four$-$year university education. The daughter recently received GH& $7,500$

from her grandfathers, estate; this money will be invested at a rate of $8\%$ to help meet the costs of

the daughter's education. The rest of the costs will be met by money the father will deposit in a

savings account which also earns $8$ percent compound interest per year. He will make $5$ equal

deposits into the account, one deposit per annum starting one year from now until his daughter

starts university. These deposits will begin one year from now. $($Assume that school fees are paid

at the beginning of the year$)$

i$)$ What will be the present value of the cost of $4$ years of education at the time the daughter

turns $18?$

ii$)$ What will be value of the GH& $7,500$ that the daughter received from her grandfather's

estate when she starts college at $18?$

iii$)$ If the father is planning to make the first of $5$ deposits one year from now, how large must

each deposit be for him to able to put his daughter through college?