Amount of tution semiannual expenses (P)=Â Â
40000
time in Semiannual periods (n) = 4*2=Â Â 8
interest rate per Semiannual year (r) = 9%/2 or Â
0.045
Tution expenses is paid at beginning. So Present value of expenses
at beginning of 18 years shall be calculated by PV of Annuity due
formula. Â
Present value of annuity due formula =P + (P* (1-
(1/(1+i)^(n-1)))/i)Â Â
=40000+(40000*(1-(1/(1+0.045)^(8-1)))/0.045)Â Â
=275708.0376Â Â
 Â
So Amount required 18 years =Â Â $275,708.04
This is now Future value for Present value Â
Interest rate Semiannual (i)=Â Â 0.045
no of Semiannual periods in 18 years (n)=18*2=Â Â 36
 Â
Present value formula = Future Value/(1+i)^n Â
$275,708.04 /(1+0.045)^36
=56527.91552Â Â
 Â
So university will accept $56,527.92 in lieu of tution starting
from 18 years Â
 Â
 Â
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