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 .You currentl 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)$1,477.02
D)$1,507.81
E)$1,622.33

Question

Quizplus · Accepted Answer

The future value of the current savings of $25,000, after 10 years with an interest rate of 6% (after taxes), would be:

FV = $25,000 x (1 + 6%)^10 = $25,000 x 1.791 = $44,775.67

To calculate the required annual contribution, we need to use the future value of an annuity formula:

FV = PMT x [(1 + r)^n - 1] / r

where PMT is the constant annual contribution, r is the interest rate per period (5%), and n is the number of periods (10).

Solving for PMT, we get:

PMT = FV x r / [(1 + r)^n - 1] = $44,775.67 x 5% / [(1 + 5%)^10 - 1] = $1,393.42

Therefore, you should contribute $1,393.42 at the beginning of each of the next 10 years to fully provide for your child's college education.

You Are Currently Saving for Your Child's College Education