The New Jersey lotto awarded a prize of $560,000 a year for the next 20 years starting today. If the state sold $21,900,000 in lotto tickets, what proportion of the sales will the state distribute if it earns 8% annually on invested funds??
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This problem illustrates the present value of an annuity due. The present value of the promised payments is $560,000(9.818)(1.08) = $5,937,930.??9.818 is the interest factor for the present value of the ordinary annuity at 8% for 20 years, and the 1.08 converts the interest factor into the interest factor for an annuity due.The state will distribute 27.1 percent of the ticket sales: $5,937,930/$21,900,000 = 27.1%.?
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