The semiannual tuition payment at a major university is expected to be $40,000 for the 4...

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

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4.1 Ratings (713 Votes)

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