Question: You rich godfather hasoffered you a choice of one of the three followi
ID: 2662567 • Letter: Q
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Question: You rich godfather hasoffered you a choice of one of the three followingalternatives: $10,000 now; $2,000 a year for eight years; or$24,000 at the end of eight years. Assuming you could earn 11percent annually, which alternative should you choose? If youcould earn 12 percent annually, would you still choose the samealternative? FYI: The FV info for $10,000 for eight years at 11 and12% is, 2.305 and 2.476. I have to show my work on this one. Please help! Question: You rich godfather hasoffered you a choice of one of the three followingalternatives: $10,000 now; $2,000 a year for eight years; or$24,000 at the end of eight years. Assuming you could earn 11percent annually, which alternative should you choose? If youcould earn 12 percent annually, would you still choose the samealternative? FYI: The FV info for $10,000 for eight years at 11 and12% is, 2.305 and 2.476. I have to show my work on this one. Please help!Explanation / Answer
Alternative 1: Present value = $10,000; No. of years = 8;Interest rate = 11%
The formula for calculating Future value (FV) is
FV = PV (1+ i)n
FV = $10,000(1+0.11)8 = $10,000(2.305) = $23,050
At i=12%, we get
FV = $10,000(1+0.12)8 = $10,000(2.476) = $24,760
Alternative 2: Given fixed number of payments for 8years. So, we have to calculate
Future value of annuity.
PMT =$2,000; n=8yrs; i=11%
The formula for calculating Future value of annuity is
FVa = PMT [{(1+i)n – 1}/i]
FVa = $2000[(2.305-1) / 0.11] = $2000(11.864) =$23,728
At i=12%
FVa = $2000[(2.476-1)/0.12] = $24,600
Alternative3: In the alternative, the Future value isgiven as $24,000
Conclusion: At 11% interest rate, alternative 2 is thebest option because the future value is high in alternative2 thanin alternative1.
At 12% interest rate, alternative 1 is the best option becausethe future value is high in alternative 1 when compared toalternative 2.
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