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Daredevil Dave, a famous skydiver, is your client. “Double D“ as he is known, comes to you and tells you that in 18 months he is planning on doing his most dangerous dive yet: a free fall from an orbiting space station. Double D says that he doesn’t have life insurance and in case he doesn’t survive this space dive, he wants to make sure his family will be provided for. He wants them to receive a monthly payment of $5,000 in perpetuity. He asks you how much money he will need to pay now in order to achieve this. Assuming a 2% rate of return, and assuming this is going to be Double D’s last dive, you tell him that he will need to contribute:
A. $3 million
B. $6 million
C. $9 million
D. $12 million
Correct Answer: A. $3 million
Rationale: A perpetuity is an annuity or stream of payments without end. To calculate the present value of a perpetuity, you divide the periodic payment by the rate of return (also known as interest rate or yield). In this case there are two ways to reach the answer: (1) Divide the 2% rate of return by 12 to get the monthly rate of return: 0.001667, then divide the monthly payment by the monthly rate of return: $5,000/0.001667 = $2,999,400 or (2) Multiply $5,000 times 12 months to get a $60,000 annualized payment to the family and then divide that by the 2% yield or $60,000/.02 = $3 million.
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