The Illinois lottery has an instant game that promises 25 top prizes of $1 milli

Question

The Illinois lottery has an instant game that promises 25 top prizes of $1 million each. In the small print it says that the $1 million prize will be paid $50,000 a year for 20 years or as a cash payment of $600,000 in lieu of the annuity. Assuming the first of the twenty $50,000 payments begins at the time the winning ticket is submitted. A.) What inrest rate was used to arrive at the $600,000 cash option. B.) If the best rate at which you could invest the cash is 4.5% p.a, is the cash option a good deal?

Explanation / Answer

A) Present value of annuity = $600,000

$600,000 = 50000 + 50000/(1+r) + 50000/(1+r)^2 + 50000/(1+r)^3 ........50000/(1+r)^19

interest rate, r= 6.18%

B)Present value ofannuity at 4.5%pa = 50000 + 50000/(1+4.5%) + 50000/(1+4.5%)^2 + 50000/(1+4.5%)^3 ........50000/(1+4.5%)^19 =

Present value ofannuity at 4.5%pa > cash option

No, cash option is not a good deal

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