SOLUTION: Marissa has just won the Cash for Life lottery. She must decide between two prize options:
- collect a lump-sum payment of $1 million, or
- receive $1000 every week for 25
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Question 1202556: Marissa has just won the Cash for Life lottery. She must decide between two prize options:
- collect a lump-sum payment of $1 million, or
- receive $1000 every week for 25 years.
After researching her options she concludes that she can safely earn 4%/a interest if she invests the $1 million in a combination of risk-free GICs and Mutual Funds. This would allow her to pay herself every week for 25 years while earning interest (compounded weekly) on the remaining balance.
a) How much would she receive each week if she invested the money herself?
b) Which option should she select? How much more money does this option provide over the life of the payments?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
her lump sum payment is 1,000,000 right away.
her investment interest rate is 4% per year compounded weekly = .0769230769% per week.
the number of weeks is 25 years * 52 weeks per year = 1300 weeks.
at the end of the 1300 weeks, she would have 2,717,237.07 in her account.
if she took the 1000 payment at the end of each week for 1300 weeks at the same inteeest rate per week, and reinvested what she received at the end of each week until the end of the investment period, she would have 2,232,408.19 in her account.
it looks like the lump sum payment gives her $484,828.88 more at the end of the 25 year investment period, given the interest rates per week are the same.
you could also have analyzed this by taking the present value of the payments.
that would have been equal to 821,572.85.
since it is less than the present value of 1 million, the 1,000,000 lump sum payment right away provides more money than the 1000 payments at the end of each week.
an excel analysis provides the same results, as shown below.
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