Question

Growing Annuity [LO1] You have just won the lottery and will receive $1,500,000 in one year. You will receive payments for 30 years, and the payments will increase by 2.7 percent per year. If the appropriate discount rate is 6.8 percent, what is the present value of your winnings?

Answer 1

Present value = initial payment *(1-(1+ growth rate /1+ discount rate )^n)/ (discount rate - growth rate)

=1,500,000[(1-((1+0.027)/(1+0.068))^30/(0.068-0.027)]

=1,500,000*(1-(0.309012271974 )/0.041

= 1,500,000*(0.690987728026)/0.041

= 1,500,000*16.85335922015

= 25280038.83