The semiannual tuition payment at a major university is expected to be $30,000 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 6%, compounded semiannually, and that tuition is paid at the end of each half-year for 4 years. (Round your answer to the nearest cent.)

$49,216.78

Step-by-step explanation:

A(n,k) = R[1-(1+i)^-n / i) (1+i)^-k

A = Present value of deferred annuity

R = Payment at the end of period

R = 30,000

i = 0.06 / 2

n = (4)*2 = 8

k = deferred period, (18)*(2) = 36

A(n,k) = 30,000*(1-(1+0.04)-^8 / 0.04)*(1+0.04)^-36

A(n,k) = 30,000*(1-(1.04)^-8 / 0.04)*(1.04)^-36

A(n,k) = 30,000*(1 - 0.730690205/0.04) * 0.24366872185

A(n,k) = 30,000*(0.269309795 / 0.04)*0.24366872185

A(n,k) = 30,000*6.732744875*0.24366872185

A(n,k) = 49216.78014700164

A(n,k) = $49,216.78

So the lump sum payment that the university accept now is $49,216.78

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