A lottery offers two options for the prize. (7)
Option A: $1000 a week for life.
Option B: $600 000 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 monthly.
Which option would the winner choose if s/he expects to live for another 50 years?
At what point in time is Option A better than Option B?
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).
To determine which option is better, we need to compare the present value of Option A with the present value of Option B, considering the time value of money and the potential investment opportunity.
Let's calculate the present value of Option A first, which is $1000 a week for life. Since the winner expects to live for another 50 years, we multiply the annual payment by the number of years, considering that there are 52 weeks in a year.
Present Value of Option A = ($1000/week) * (52 weeks/year) * (50 years)
Now, let's calculate the present value of Option B, taking into account the investment opportunity. The winnings of $600,000 can be invested at a compounded monthly interest rate of 3%/a.
To calculate the present value of Option B, we can use the present value of an annuity formula:
PV = PMT * [(1 - (1 + r)^(-n)) / r]
Where:
PV is the present value
PMT is the monthly payment
r is the monthly interest rate
n is the total number of monthly payments
First, we need to find the monthly payment that can be made using the winnings over 50 years. We can use the formula for the future value of an annuity:
FV = PMT * [(1 + r)^n - 1] / r
We know:
FV = $600,000
r = 3%/12 (monthly interest rate)
n = 50 * 12 (total number of monthly payments)
Rearranging the formula to solve for PMT gives us:
PMT = FV * r / [(1 + r)^n - 1]
Now we can calculate the present value of Option B using the present value of an annuity formula mentioned earlier.
Present Value of Option B = PMT * [(1 - (1 + r)^(-n)) / r]
Once we have both present values, we can compare them.
To determine at what point Option A becomes better, we need to calculate the present value of Option A and Option B for various time periods until Option A surpasses Option B. We can compare the present value at certain intervals, such as every 10 years.
As for which option to choose and reflecting on it, consider your financial goals, risk tolerance, and spending habits. Option A provides a consistent stream of income for life, which can be more reliable for those who want a stable income stream. Option B offers a lump sum that can be invested, potentially earning additional returns. Reflect on your financial needs, long-term plans, and personal preferences to make the decision that aligns with your goals and values. Additionally, you may want to consult with a financial advisor who can provide personalized advice based on your specific situation.