If you won $2,5 million in a lottery. You can receive $1.3million now or $100,000 at the end of each of the next 25 years, You can earn 5% annually on the investments . Which is the better option?
To determine which option is better, we need to compare the present value of the two options. Present value is the current value of future cash flows, taking into account the time value of money.
Option 1: Receiving $1.3 million now.
Option 2: Receiving $100,000 at the end of each of the next 25 years.
To calculate the present value of the cash flows in option 2, we can use the formula for the present value of an ordinary annuity:
PV = C * [(1 - (1+r)^(-n)) / r]
Where:
PV = Present value
C = Cash flow per period ($100,000)
r = Interest rate per period (5% or 0.05)
n = Number of periods (25)
By plugging the values into the formula, we can find the present value of the cash flows in option 2.
Now, let's calculate the present value for both options and compare:
Option 1: $1.3 million (no calculations needed)
Option 2:
PV = $100,000 * [(1 - (1+0.05)^(-25)) / 0.05]
≈ $1,687,268.70
Comparing the two options, we find that the present value of option 2 is approximately $1,687,268.70, while option 1 is $1.3 million.
Therefore, the better option is to choose option 1, receiving $1.3 million now.