6. A lottery offers two options for the prize.
Option A: $1000 a week for life
Option B: $ 600 000 in one lump sum.
The current expected rate of return for large investment is 7%/a, compounded weekly.
a. Which option would the winner choose if s/he expects to live for another 25 years?
so you need to find the Present Value of $1000 per week for 25 years.
i = .07/52 = .001346153
n = 25(52) = 1300
evaluate
1000( 1 - 1.001346153^-1300)/.001346153
and compare to $600 000
To determine which option the winner would choose, we need to compare the present value of Option A (the weekly payments) to the lump sum of Option B. Since the expected rate of return is 7% compounded weekly, we can use the present value formula to calculate the present value of Option A.
The present value formula is given by:
PV = FV / (1 + r)^n
Where:
PV = Present value
FV = Future value
r = Interest rate per compounding period
n = Number of compounding periods
For Option A, we need to calculate the present value of $1000 received every week for the remaining 25 years.
First, we need to find the total number of weeks in 25 years. There are 52 weeks in a year, so:
Total weeks = 25 years * 52 weeks/year = 1300 weeks
Next, we can plug the values into the present value formula:
PV_A = $1000 / (1 + 0.07/52)^(1300)
Now, we can calculate the present value of Option A.
PV_A = $1000 / (1 + 0.001346)^1300 ≈ $464,218.86
For Option B, the winner receives a lump sum of $600,000. Since this is the current value, we don't need to calculate the present value.
Now, we can compare the present value of Option A to the lump sum of Option B to determine which option the winner would choose.
If PV_A > Option B, then the winner would choose Option A.
If PV_A < Option B, then the winner would choose Option B.
Comparing the values, $464,218.86 (PV_A) < $600,000 (Option B).
Therefore, if the winner expects to live for another 25 years, they would choose Option B, which is the $600,000 lump sum.