You have just won the lottery and will receive 600000 in one

You have just won the lottery and will receive $600,000 in one year. You will receive payments for 29 years, which will increase 5 percent per year. The appropriate discount rate is 12 percent. What is the present value of your winnings?

Solution

Present value of a growing annuity = P/(r - g) * (1 - ((1+g)/(1+r)ⁿ)

Present value of a growing annuity = 600,000/(0.12 - 0.05) * (1 - (1.05/1.12)^29)

Present value of a growing annuity = 7,252,503.19