Question

You are currently saving for your child's college education. The current cost of college is $10,000 a year. You expect that college costs will continue to increase at a rate of 5 percent a year. Your child is scheduled to begin attending a four-year college 10 years from now (i.e., college payments will be made at t=10, t=11, t=12, and t=13). You currently have $25,000 in an account which earns 6 percent after taxes. You would like to have all of the necessary savings by the time your child enters college, and you would like to contribute a constant amount at the beginning of each of the next 10 years in order to provide the necessary amount. (You want to make 10 equal contributions starting in Year 0 and ending at Year 9.) How much should you contribute to the account each year in order to fully provide for your child's education?

a. $1,133.16

b. $1,393.42

c. $1,622.33

d. $1,507.81

e. $1,477.02

Answer 1

1. Cost of College Fees at the time of joining college:

T10 = Current Cost * (1 + r)^10 = 10000 * 1.05^10 = 16288.95

T11 = T10 * (1 + r) = 16288.95 * 1.05 = 17103.39

T12 = T11 * (1 + r) = 17103.39 * 1.05 = 17958.56

T13 = T12 * (1 + r) = 17958.56 * 1.05 = 18856.49

2. Present Value of College Costs = 16288.95 / (1 + r)^10 + 17103.39 / (1 + r)^11 + 17958.56 / (1 + r)^12 + 18856.49 / (1 + r)^13

Present Value of College Costs = 16288.95 / (1.06)^10 + 17103.39 / (1.06)^11 + 17958.56 / (1.06)^12 + 18856.49 / (1.06)^13

Present Value of College Costs = 35871.03

3. Net Amount needed over 10 years = 35871.03 - 25000 = $10871.03

4. Contribution per Year = Amount needed / PVAD (0.06,10)

Contribution per Year = 10871.03 / 7.8017

Contribution per Year = $1393.42 Option B