q$.$ ay$$e and ahmet are interested in saving money to put their child nehir to

college. Nehir is $10$ years old, and will enter college in $8$ years and plan to

finish college in $4$ years.

College costs are currently $15\mathrm{.}000$ dollars anda re expected to increase by

$500$ dollars per year. All the college costs are paid at the beggining of the

school year. Up until now, ayse and ahmet have saved nothing. However,

they expect to make $12$ equal payments at the beggining of each of the

next $12$ year.s the first payment will be mde today adn the final payment

will be made on nehirs $21$ st birthday $($ which is also the last day that the

last paymeny must be made to college$)$ suppose that all funds are

invested in a bank account that is expected to provide a $12$ percent rate

of return.

a$.$ Calculate the cost of nehirs college education in each year. Whats the

present value of her college education.

b$.$ Calcualte the annual payments that ayse and ahmet need to deposit

to finance the college.

c$.$ Suppose that nehirs grandma is to give her $20\mathrm{.}000$ dollars for her

college education when she turns $15.$ How much do they need to save

each year if ayse and ahmet deposit this gift to the same bank accoun?