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The state? lottery's million-dollar payout provides for ?$1
The state? lottery's million-dollar payout provides for ?$1.3 million to be paid in 25 installments of ?$52,000 per payment. The first ?$52,000 payment is made? immediately, and the 24 remaining ?$52,000 payments occur at the end of each of the next 24 years. If 16 percent is the discount? rate, what is the present value of the cash? flows?
a. If 8 percent is the discount? rate, the present value of the annuity due is ?$_____ ?(Round to the nearest? cent.)
Expert Solution
Computation of the present value of the annuity due if the discount rate is 8%:-
Present value of annuity due = Annual payment * ((1-(1+r)^-n)/r) *(1+r)
= $52,000 * ((1-(1+8%)^-25)/8%)*(1+8%)
= $52,000 * 10.67478 * 1.08
= $599,495.43 Or $599,495
Computation of the present value of the cash flows if the discount rate is 16%:-
Present value of cash flows = Annual payment * ((1-(1+r)^-n)/r) *(1+r)
= $52,000 * ((1-(1+16%)^-25)/16%)*(1+16%)
= $52,000 * 6.09709 * 1.08
= $367,776.59 Or $367,777
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