Question

You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments that increase by $700,000 per year. Thus, in one year, you receive $1.70 million. In two years you get $2.40 million, and so on. If the appropriate interest rate is 8.0 percent, what is the value of your winnings today?

(Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars, and round your answer to 2 decimal places, e.g., 1,234,567.89.)

Answer 1

Present value = 1000000 + 1700000/(1+8%)^1 + 2400000/(1+8%)^2 + 3100000/(1+8%)^3 + 3800000/(1+8%)^4 + 4500000/(1+8%)^5 + 5200000/(1+8%)^6 + 5900000/(1+8%)^7 + 6600000/(1+8%)^8 + 73000000/(1+8%)^9 + 8000000/(1+8%)^10

Present value = Value of winnings today = $30,590,920.41

Alternate representation or method:

Years	Cash flows = CF	Df = discounting factor = 1/(1+8%)^Years	PVs
0	1,000,000	1.00000	1,000,000.00
1	1,700,000	0.92593	1,574,074.07
2	2,400,000	0.85734	2,057,613.17
3	3,100,000	0.79383	2,460,879.95
4	3,800,000	0.73503	2,793,113.44
5	4,500,000	0.68058	3,062,624.39
6	5,200,000	0.63017	3,276,882.06
7	5,900,000	0.58349	3,442,593.33
8	6,600,000	0.54027	3,565,774.64
9	7,300,000	0.50025	3,651,817.46
10	8,000,000	0.46319	3,705,547.90
		Total PV =	30,590,920.41