Question

You had your first child recently. You would like to set aside some funds so that your child will be able to attend the University of Texas as an undergraduate without taking on any student loans. Total costs of attendance for undergraduate students currently amount to $28,000 per year and are expected to continue to grow at a 2.5% growth rate per year. Assume that the four-year college expenses for the first year of college need to be paid exactly 18 years from today and that the subsequent costs need to be paid at an annual frequency 19, 20, and 21 years from today. You would like to make 18 equal annual payments starting today to your child’s college savings account to be able to cover the expected college costs. The savings are invested in risk-free Treasury securities that offer a return of 2%. How large are the equal annual contributions to the college savings account over the next 18 years?

Answer 1

Answer:

Equal annual contributions to the college savings account over the next 18 years is : $4,745.6

Explanation:

Suppose the time the child was born is the Beginning of Year 0 (Y0). So, 18 equal contributions need to be made at the beginning of each year from Y0 to Year 17. Denote these cash flow as Annuity 1 which equal: ( C/ 2%) x ( 1.02^18 -1) = 21.4123 x C with C is the equal annual contribution

The tuition fee starting from the beginning of Year 18 end at the Beginning of Year 21 is a growing annuity at 2.5% growth rate. The Value of this annuity ( Annuity 2) discounted to the Beginning of Year 17 calculated as followed:

(28,000 / (2% - 2.5% ) x ( 1 - [( 1+2.5%)/(1+2%)]^4 ) = $110,614

To save enough for college fee, The future value of Annuity 2 must equal the present value of Annuity 2 calculated above.

Thus, we have: 21.4123 x C = 110,614 <=> C = $4,745.6