Question 22.86

image 56. (Requires a spreadsheet) Winners of the Powerball lottery can elect either an immediate lump sum (almost all do) or an annuity. In the latter case, the advertised jackpot amount is paid in 30 annual payments, including one immediate payment. To keep up with inflation, each payment is 4% more than the previous year’s; such an annuity is called a graduated annuity. On October 10, 2007, Eugene and Stanislawa Markiewicz took their prize of $20 million in the form of a graduated annuity.

  1. What was the amount of their first payment, and how much will they receive in their last payment in October 2036?
  2. The winners could have chosen a lump sum of $9,402,914.90 instead. What was the corresponding interest rate of the annuity?