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Alex Meir recently won a lottery and has the option of receiving one of the following three prizes: (1) $70,000 cash immediately, (2) $24,000 cash immediately and a six-period annuity of $8,100 beginning one year from today, or (3) a six-period annuity of $14,500 beginning one year from today. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1). 1. Assuming an interest rate of 7%, determine the present value for the above options.

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Answer:

The net present value for each option is given below.

(1) $70,000 cash immediately

NPV = 70,000 * 1 = $ 70,000

(2) $24,000 cash immediately and a six-period annuity of $8,100 beginning one year from today, or

NPV = (24,000*1) + (8,100 *(1-((1+7%)^-6)/7%)) = $ 62,609

(3) a six-period annuity of $14,500 beginning one year from today

NPV = (14,500 *(1-((1+7%)^-6)/7%)) = $ 69,115

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