A father and mother are planning a savings program to put their daughter through college. Their daughter is now $8$ years old. She plans to enroll at the university when she is $18$ and it should take her $4$ years to complete her education. Currently, the cost per year $($for tuition, etc.$)$ is $$16,200,$ but a $2$ percent inflation rate in these costs is forecasted. The cost for each year of college will be withdrawn when she turns $18,19,20,$ and $21.$

The daughter received $$13,000$ at age $4$ and another $$2,900$ at age $6$ from her grandmother; this money, which is invested in an account earning $7\mathrm{.}5$ percent interest compounded annually, will be used to help meet the costs of the daughter's education. The rest of the costs will be met by money the parents will deposit in the savings account. They will make $4$ equal annual deposits to the account, with the first deposit being made today on her $8$th birthday and the last one being made on her $11$ th birthday. These deposits will also earn $7\mathrm{.}5$ percent interest compounded annually. How large must each deposit $($from the parents$)$ be in order to put the daughter through college? $($Round cash flows to nearest dollar throughout.$)$

a$.$ $$5,126$

b$.$ $$4,629$

c$.$ $$4,103$

d$.$ $$5,657$

e$.$ None of the above is within $$10$ of the correct answer.