Answer:
$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
