Question

​(Present value of annuity​ payments) The state​ lottery's million-dollar payout provides for ​$1 million to be paid in 20 installments of ​$50,000 per payment. The first ​$50,000 payment is made​ immediately, and the 19 remaining ​$50,000 payments occur at the end of each of the next 19 years. If 6 percent is the discount​ rate, what is the present value of this stream of cash​ flows? If 12 percent is the discount​ rate, what is the present value of the cash​ flows?

a.  If 6 percent is the discount​ rate, the present value of the annuity due is ​$. ​(Round to the nearest​ cent.)

b. If 12 percent is the discount​ rate, the present value of the annuity due is ​$. ​(Round to the nearest​ cent.)

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

B $50,000.00 Annual payment Total No. annual payments First payment Remaining 19 payments immediately end of each next 19 years a. Discount rate Present value of annuity due 6% $607,905.82 b. Discount rate Present value of annuity due 12% $418,288.84 11 12 13

Cell reference -

L2T . 50000 20 Annual payment Total No. annual payments First payment Remaining 19 payments immediately end of each next 19 years a. Discount rate Present value of annuity due 0.06 =PV(C7,C3,-C2,,1) b. Discount rate Present value of annuity due 0.12 =PV(C10,C3,-C2,,1)

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.