Posted by Anonymous on Sunday, July 31, 2011 at 6:20pm.
Sally has won the grand prize in a lottery and must choose between the following three options:
A. Receive a lump sum payment of $10,000,000
B. Receive annual end of year payments $2,000,000 for the next 8 years:
C. Receive annual end of the year payments of $1,500,000 for the next 20 years:
Which option should Sally chose based on annual investment of rate of 6%?

MBA Finance  Ms. Sue, Sunday, July 31, 2011 at 6:24pm
First  there's no guarantee today that the investment rate is or will ever be 6% again.
Second, option C. is out if Sally is elderly.
What do you think?

MBA Finance  MathMate, Sunday, July 31, 2011 at 7:38pm
Assume a constant investment rate of 6% indefinitely, and that Sally has a life expectancy of over 20 years.
Also, assume that the winnings are deposited the money in a trust fund independent of the lottery company.
A.
Future value at the end of 8 years
=10M*1.06^8
=15.938M$
Future value at the end of 20 years
=32.071M$
B. future value of 8 yearly payments
=2M$*(1.06^81)/(1.061)
=19.795M$ > 15.93 M$
i.e. better choice than A.
C. Future value of 20 yearly payments of 1.5M$
=1.5*(1.06^201)/(1.061)
=55.178M$ > 32.07M$
i.e. better choice than A.
Now compare B and C by investing the future value of B (after 8 years) for the following 12 years at 6%.
Future value of option B after 12 more years
= 19.795M$ * 1.06^12
= 39.831M$ < 55.178M$
Thus option C is by far the most advantageous, assuming all the preconditions are met.
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