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