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?