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 calculate the present value of both scenarios to compare them fairly. The present value tells us how much the future cash flows are worth in today's dollars, considering the time value of money and the investment return rate of 5% annually.
Option 1: Receiving $1.3 million now.
Option 2: Receiving $100,000 at the end of each of the next 25 years.
Let's start by calculating the present value of Option 1, where you would receive $1.3 million now:
Present Value (Option 1) = $1.3 million
For Option 2, we need to calculate the present value of each $100,000 payment and then sum them up:
Present Value (Option 2) = Present Value (Payment 1) + Present Value (Payment 2) + ... + Present Value (Payment 25)
Using the formula for calculating the present value of an annuity, we can determine the present value of each payment:
Present Value (Payment) = Payment / (1 + interest rate)^n
Where:
Payment = $100,000
Interest rate = 5%
n = number of years from now the payment is received
Calculating each Present Value (Payment) for Option 2:
Present Value (Payment 1) = $100,000 / (1 + 0.05)^1
Present Value (Payment 2) = $100,000 / (1 + 0.05)^2
...
Present Value (Payment 25) = $100,000 / (1 + 0.05)^25
Now, we can sum up all the Present Value (Payment) to get the overall Present Value (Option 2).
Finally, compare the Present Value (Option 1) with the Present Value (Option 2). If the Present Value (Option 1) is higher, receiving $1.3 million now is the better option. If the Present Value (Option 2) is higher, receiving $100,000 at the end of each year for 25 years is the better option.
By performing these calculations, you can determine which option provides the higher present value and make an informed decision.