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 the better option between receiving a lump sum now or payments over 25 years, we need to calculate the present value of the two options and compare them.
First, let's calculate the present value of the $1.3 million lump sum. Since you can earn a 5% annual return on investments, we'll use that rate as the discount rate for calculating the present value. The formula to calculate the present value is:
PV = FV / (1 + r)^n
Where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods.
Using this formula, the present value of a lump sum payment of $1.3 million is:
PV = 1,300,000 / (1 + 0.05)^0
PV = 1,300,000 / 1
PV = 1,300,000
So, the present value of the lump sum is $1.3 million.
Now let's calculate the present value of receiving $100,000 at the end of each of the next 25 years. We will calculate the present value of each payment and sum them up.
PV = Payment 1 / (1 + r)^1 + Payment 2 / (1 + r)^2 + ... + Payment n / (1 + r)^n
Substituting the values into the formula, we get:
PV = 100,000 / (1 + 0.05)^1 + 100,000 / (1 + 0.05)^2 + ... + 100,000 / (1 + 0.05)^25
Using a financial calculator or spreadsheet, we can calculate this sum. The present value of the annuity payments is approximately $1,959,832.
Comparing the present values, we have $1.3 million for the lump sum option and $1,959,832 for the annuity payments option. Since the annuity payments have a higher present value, it is the better option financially.
Therefore, in this scenario, it is better to choose the $100,000 at the end of each of the next 25 years instead of the $1.3 million lump sum.