You have just won the lottery and will receive $540,000 as your first payment one year from now.You will receive payments for 26 years.The payments will increase in value by 4 percent each year.The appropriate discount rate is 10 percent.What is the present value of your winnings?

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Quizplus · Accepted Answer

The present value of the winnings can be calculated using the formula for the present value of a growing annuity. The formula is: PV = P * [(1 - (1 + g)^n / (1 + r)^n) / (r - g)], where P is the first payment, g is the growth rate, n is the number of payments, and r is the discount rate. Plugging in the values: P = $540,000, g = 4% or 0.04, n = 26, and r = 10% or 0.10, we get the present value of the winnings. Calculating with these inputs gives a present value of approximately $6,906,372, which matches option B.

You Have Just Won the Lottery and Will Receive $540,000