13. -12 points SApCalcBr1 6.2.031 My Notes Ask Your Teacher The winner of a lott

Question

13. -12 points SApCalcBr1 6.2.031 My Notes Ask Your Teacher The winner of a lottery is awarded $6,000,000 to be paid in annual installments of $300,000 for 20 years. Alternatively, the winner can accept a "cash value" one-time payment of $2,700,000. The winner estimates he can earn 8% annually on the winnings, what is the present value of the installment plan? (Round your answer to two decimal places.) Should he choose the one-time payment instead? Yes, he should choose the one-time payment. No, he should not choose the one-time payment.

Explanation / Answer

Hi,
Present value of annuity needs to be calculated in this to choose an option ,
it is given by the formula
P*(1-(1+r)-n)/(r) i.e 300000* (1-(1+0.08)-20)/0.08 =2,945,444.2 $
therefore he should NOT choose the one time payment option as its less than above value

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