Question

Consider a lottery that pays to the winner an annuity of $500 that begins immediately (an annuity due) and then annually in year 1 through year 16 with one exception. Because of high administrative costs associated with running the lottery, the payment in year 11, and only 11, is not $500 but $0. Using an interest rate of 8%, determine the present value of this cash flow stream.

Answer 1

The present value of an annuity that pays $500 per year from year 1 - 16 is $4711.24

An annuity can be defined as the payment of a specified amount of money for a stated period.

Present value is the value of the discounted cash flows at time zero

Present value is the sum of the discounted cash flows from year 1 to 16

Present value in year 0 = $500

Present value in year 1 =  $500 / (1.08) = 462.96

Present value in year 2 = $500 / (1.08^2) = 428.67

Present value in year 3 = $500 / (1.08^3) =396.92

Present value in year 4 = $500 / (1.08^4) = 367.51

Present value in year 5 = $500 / (1.08^5) =340.29

Present value in year 6= $500 / (1.08^6) = 315.08

Present value in year 7 = $500 / (1.08^7) =291.45

Present value in year 8 = $500 / (1.08^8) = 270.13

Present value in year 9 = $500 / (1.08^9) = 250.12

Present value in year 10 = $500 / (1.08^10) = 231.60

Present value in year 11 = 0

Present value in year 12 = $500 / (1.08^12) =198.56

Present value in year 13 = $500 / (1.08^13) =183.85

Present value in year 14 = $500 / (1.08^14) =170.23

Present value in year 15 = $500 / (1.08^15) =157.62

Present value in year 16 = $500 / (1.08^16) =145.95

Sum of present values is $4711.24

A similar question was solved here: brainly.com/question/9641711?referrer=searchResults