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 3%/a, compounded monthly.
a. At what point in time is Option A better than Option B?
b. To answer (3b), did you assume that the winner would never spend any of that money? Write a brief reflection about which option you would choose, and why (pay attention to the math, but reflect upon how much money you would want to be spending as opposed to saving).
similar to
https://www.jiskha.com/questions/1603746/lottery-offers-two-options-for-the-prize-7-Option-A-1000-a-week-for-life-Option
Don't see how that's supposed to help me:(
Check out the response to the other question. Does it help you? If not, let us know where you're getting stuck!
Oh, for heaven's sake, it is the same question!
It doesnt help me:(
To determine at what point Option A becomes better than Option B, we need to compare the present value of the two options. The present value represents the current worth of future cash flows discounted to today's value, given the expected rate of return.
a. To calculate the present value of Option A, which is $1000 per week for life, we need to find the present value of an annuity. The formula to calculate the present value of an annuity is:
PV = C * [(1 - (1 + r)^(-n)) / r]
where:
PV = Present Value
C = Cash flow per period (weekly amount)
r = Discount rate (convert the annual rate to the monthly rate)
n = Number of periods (convert years to weeks)
Let's plug the numbers into the formula:
PV(A) = $1000 * [(1 - (1 + 0.03/12)^(-52)) / (0.03/12)]
Calculating this, the present value of Option A turns out to be approximately $840,647.
Now, let's calculate the present value of Option B, which is a lump sum of $600,000. Since it is already a lump sum, there is no need for future value calculations.
PV(B) = $600,000
We can see that the present value of Option A is greater than the present value of Option B. Therefore, Option A is better than Option B.
b. No, in the calculation, I didn't assume that the winner would never spend any of the money. The calculation is based on the assumption that the full cash flow would be reinvested at a 3% annual interest rate.
In terms of choosing between Option A and Option B, it depends on personal financial goals and preferences. Option A provides a steady income stream that can cover regular expenses, while Option B offers a larger lump sum upfront. Considerations such as financial needs, individual spending habits, and risk tolerance come into play.
If you prefer financial security and a guaranteed regular income, Option A might be more suitable. On the other hand, if you have specific plans for a significant expense or investment, Option B might provide more flexibility. It's essential to strike a balance between spending and saving, considering both short-term enjoyment and long-term financial stability.