Question

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 The cost for each year of college will be withdrawn when she turns 18, 19, 20, and 21.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 7.5 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 8th birthday and the last one being made on her 11th birthday. These deposits will also earn 7.5 percent interest compounded annually. How large must each deposit (from the parents) be in order to put the daughter through college

Answer 1

Answer:

$4,102.57

Explanation:

we must first calculate the future costs of college:

cost of college year 1 = $16,200 x (1 + 2%)¹⁰ = $19,747.71

cost of college year 2 = $19,747.71 x 1.02 = $20,142.66

cost of college year 3 = $20,142.66 x 1.02 = $20,545.51

cost of college year 4 = $20,545.51 x 1.02 = $20,956.42

in order to determine how much money does the family need to have before college starts we must discount the cost of college by 7.5%:

PV cost of college year 1 = $19,747.71

PV cost of college year 2 = 20,142.66 / 1.075 = $18,737.36

PV cost of college year 3 = $20,545.51  / 1.075² = $17,778.70

PV cost of college year 4 = $20,956.42  / 1.075³ = $16,869.09

total = $73,132.86

the future value of the grandmother's deposits:

$13,000 x (1 + 7.5%)¹⁴ = $35,781.77

$2,900 x (1 + 7.5%)¹² = $6,907.16

total = $42,688.93

that means that you will need to save $73,132.86 - $42,688.93 = $30,443.93 by the time your child turns 18

you will make 4 deposits and their future value will be:

deposit x 1.075¹⁰ = 2.0610D

deposit x 1.075⁹ = 1.9172D

deposit x 1.075⁸ = 1.7835D

deposit x 1.075⁷ = 1.6590D

total = 7.4207D

yearly deposit = $30,443.93 / 7.4207 = $4,102.57