Question

The semiannual tuition payment at a major university is expected to be $40,000 for the 4 years beginning 18 years from now. What lump sum payment should the university accept now, in lieu of tuition payments beginning 18 years, 6 months from now? Assume that money is worth 9%, compounded semiannually, and that tuition is paid at the end of each half-year for 4 years. (Round your answer to the nearest cent.)

Answer 1

Amount of tution semiannual expenses (P)=   40000
time in Semiannual periods (n) = 4*2=   8
interest rate per Semiannual year (r) = 9%/2 or   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.  

Present value of annuity due formula =P + (P* (1- (1/(1+i)^(n-1)))/i)  
=40000+(40000*(1-(1/(1+0.045)^(8-1)))/0.045)  
=275708.0376  
  
So Amount required 18 years =   $275,708.04
This is now Future value for Present value  
Interest rate Semiannual (i)=   0.045
no of Semiannual periods in 18 years (n)=18*2=   36
  
Present value formula = Future Value/(1+i)^n  
$275,708.04 /(1+0.045)^36
=56527.91552  
  
So university will accept $56,527.92 in lieu of tution starting from 18 years