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$*(1.06^8-1)/(1.06-1)

=19.795M$ > 15.93 M$

i.e. better choice than A.

C. Future value of 20 yearly payments of 1.5M$

=1.5*(1.06^20-1)/(1.06-1)

=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 pre-conditions are met.

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