To get the annual payments, you first have to calculate the college fees’ total required amount.
Step 1; Calculate the current cost for the 4 years in college
Current cost for year 1
Current college cost (1 + Growth rate)n
Where
Current college cost = 18,000
Growth rate = 3% = 0.03
n = 13(number of years the daughter will take to enroll in college)
= 18,000 (1 + 0.03)13
= 18,000 (1.03)13
= 18,000 x 1.4685337
= 26,433.6068
Current cost for year 2
= Current cost for year 1 x (1 +0.03)
= 26,433.6068 x 1.03
= 27,226.6150
Current cost for year 3
= Current cost for year 2 x (1 +0.03)
= 27,226.6150 x 1.03
= 28,043.4135
Current cost for year 4
= Current cost for year 3 x (1 +0.03)
= 28,043.4135 x 1.03
= 28,884.7159
Step 2; Calculate the present value of the current cost 13 years from now
The present value of the current cost for year 1
= 26,433.6068
Present value of the current cost for year 2
= 27,226.6150 / (1 + 0.08)
= 27,226.6150 / 1.08
= 25,209.8287
Present value of the current cost for year 3
= 28,043.4135 / (1 + 0.08)2
= 28,043.4135 / (1.08)2
= 24,042.7070
Present value of the current cost for year 4
= 28,884.7159 / (1 + 0.08)3
= 28,884.7159 / (1.08)3
= 22,929.6188
Step 3; Calculate the total present value of the current cost
= 26,433.6068 + 25,209.8287 + 24,042.7070 + 22,929.6188
= 98,615.7613
Step 4; Calculate the future value of the Fathers Current savings
FV = P ( 1 + r )n
Where
P = 10,000
r = 8% = 0.08
n = 13
= 10,000 ( 1 + 0.08)13
= 10,000 (1.08)13
= 27,196.2373
Step 5; Calculate the required amount
Required amount = total present value of the current cost – future value of the Fathers Current savings
Where
Total present value of the current cost = 98,615.7613
Future value of the Fathers Current savings = 27,196.2373
= 98,615.7613 – 27,196.2373
= 71,419.524
Step 6; Calculate the annual payments made
Where
FV Of Annuity = Equal payments( 1 + r )n – 1 / r
Lets assume Equal instalments = b
71,419.524 = b ( 1 + 0.08 )13 – 1 / 0.08
71,419.524 = b ( 1.08 )13 – 1 / 0.08
71,419.524 = b ( 2.7196 – 1 / 0.08 )
71,419.524 = b ( 1.7196 / 0.08 )
71,419.524 = b ( 21.494297 )
21.494297b = 71,419.524
b = 71,419.524 / 21.494297
b = 3,322.5651
b = 3,322.57
Equal payments = $3,322.57