Question

John just turned 12 (at t = 0), and he will be entering college 6 years from now (at t = 6). College tuition and expenses at State U. are currently $16,500 a year, but they are expected to increase at a rate of 3.5% a year. John is expected to graduate in 4 years. Tuition and other costs will be due at the beginning of each school year (at t = 6, 7, 8, and 9). So far, John’s college savings account contains $10,000 (at t = 0). John’s parents plan to add an additional $12,000 in each of the next 4 years (at t = 1, 2, 3, and 4). Then they plan to make 2 equal annual contributions in each of the following two years, t = 5,, and 6. They expect their investment account to earn 5.5%. How large must the annual payments at t = 5, and 6 be to cover John’s anticipated college costs?

Answer 1

Given,

Fee per year at current rate= $16,500 and annual growth rate= 3.5%

Therefore, fee in year t=6 (first year of school)= 16500*(1+3.5%)^6 = $20,282.71

(A) Amount required in year t=6 for meeting the 4 year classes is the present value of growing annuity due, ascertained at $169,297.39 as follows:

Given, current savings= $10,000 and interest rate= 5.5%

(B)    Future value of current savings in year t6 = 10,000*(1+5.5%)^6 = $13,788.43

Also given, additional savings in years 1,2,3 and 4 are $12,000 each

(C ) Future value of additional savings at year t6= [12,000*(FVIFA 5.5%, 4)]*(FVIF 5.5%,2)

=12000* 4.34226638* 1.113025 = $57,996.61

(D)   Remaining amount required as at year t6= A-(B+C)

= 169,297.39 - (13,788.43+57,996.61) = $97,512.35

Annual payments required at the end of years t=5 and t=6 = $47,451.27

Calculation as follows: