a father is now planning a savings program to put his daughter through college. she is 10, plans to enroll at the university in 8 years, and should graduate 4 years later. currently, the annual cost (for everything is $15,000, but these costs are expected to increase by 5% annually. the college requires total payment at the start of the year. she now has $10,000 in a college savings account expected to earn 10%. her father will make 8 equal annual deposits into her account; the first deposit today and the eighth on the day she starts college. how much must each of the 8 payments be?

To calculate the amount of each payment, we need to determine the total cost of the college education and the amount of money that will be in the college savings account when the daughter starts college.

First, let's calculate the total cost of the college education. The cost is currently $15,000 per year, and it is expected to increase by 5% annually. The daughter will be in college for 4 years, so the total cost of the education will be:

$15,000 * (1 + 0.05)^4 = $22,936.81

Next, let's calculate the amount of money that will be in the college savings account when the daughter starts college. The account currently has $10,000, and the father will make 8 equal annual deposits. The account is expected to earn 10% annually, so the balance after 8 years will be:

$10,000 * (1 + 0.10)^8 = $25,937.42

To pay for the entire cost of the education, the father will need to make 8 payments of:

($22,936.81 - $25,937.42) / 8 = $-2,000.81 / 8 = $-250.10

So, the father will need to make 8 payments of $250.10 each.

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