The state? lottery\'s million-dollar payout provides for ?$1.2 million to be pai

Question

The state? lottery's million-dollar payout provides for ?$1.2 million to be paid in 25 installments of ?$48,000 per payment. The first ?$48,000 payment is made? immediately, and the 24 remaining ?$48,000 payments occur at the end of each of the next 24 years. If 11 percent is the discount? rate, what is the present value of this stream of cash? flows? If 22 percent is the discount? rate, what is the present value of the cash? flows?

a.??If 11 percent is the discount? rate, the present value of the annuity due is ?$____. ?(Round to the nearest? cent.)

Explanation / Answer

present value of the annuity due=(1+interest rate)*Annuity[1-(1+interest rate)^-time period]/rate

1.Present value=(1.11)*$48000[1-(1.11)^-25]/0.11

=$48000*9.348136578

=$448,710.56(Approx).

2.Present value=(1.22)*$48000[1-(1.22)^-25]/0.22

=$48000*5.507000558

=$264,336.03(Approx).

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