A lottery offers two options for the prize. (7 marks)
Option A: $1000 a week for life.
Option B: $1 000 000 in one lump sum.
If you choose Option B, you have the opportunity to place the winnings into an investment that also makes regular payments, at a rate of 3%/a, compounded weekly. The annuity will pay out a specific amount weekly based on how long you want the annuity to last.
an image of lottery number balls
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a. Which option would the winner choose if you expect to live for another:
20 years?
50 years?
b. Use technology to determine the range of life expectancies when each option is preferred. Show your work.
c. Write a brief reflection about which option you would choose, and why.
I will do an approximate solution by assuming 4 weeks per month, thus a monthly payment of $4000
b) Are they ever equal? let that time be n months
4000(1 - (1.0025)^-n)/.0025 = 1,000,000
1 - (1.0025)^-n = .625
1.0025^-n = .375
Now, Taking logs
-n = log .375/log 1.0025 = -392.85
n = appr 392.85 months
I would answer it as 393 months and 3 weeks
c) According to a financial standpoint, i think it would clearly
depend on the number of years of expected life as calculated in a),
as that will define the present value of cash inflow. However, the
essential or immediate need of an individual may vary his/her
choice from a non-financial viewpoint. Your choice of a relaxing
retirement may lure towards the first choice, but an urgency of
funds may require you to look for Option B.
A lottery offers two options for the prize. (7 marks) Option A: $1000 a week for life. Option B: $1 000 000 in one lump sum. If you choose Option B, you have the opportunity to place the winnings into an investment that also makes regular payments, at