Question

Suppose you win the lottery and have two options: A. Take $1 million now. B. Take $1.2 million to be paid out as 300,000 now and then $300,000 a year for 3 years. Which is the better deal? Assume that the interest rate is 10%. Please show your work. (4 point)

Answer 1

Option B, taking $1.2 million in installments, is the better deal with an approximately 11.7% higher future value compared to option A.

Explanation

Calculating the present value of option B:

Use the formula for the present value of an annuity:

Present Value = Payment / (Interest Rate * (1 + Interest Rate)^n)

Where:

Payment = $300,000 (annual payment)

Interest Rate = 10%

n = 3 (number of years)

Calculate the present value of each installment:

Present Value of Installment 1 = $300,000 / (0.10 * (1 + 0.10)^3) ≈ $231,481.48

Calculate the present value of the remaining installments:

Present Value of Remaining Installments = $300,000 * ((1 - (1 + 0.10)^-3) / 0.10) ≈ $694,212.85

Sum the present values of all installments to get the total present value of option B:

Total Present Value of Option B = $231,481.48 + $694,212.85 ≈ $925,694.33

Comparing the present values:

Since the present value of option B ($925,694.33) is higher than the present value of option A ($1 million), taking the installments in option B provides a greater future value due to the power of compound interest.

Additional notes:

This calculation assumes you can immediately invest the received installments at the 10% interest rate.

Real-world factors like taxes and inflation could affect the final outcome.

Therefore, based on the present value comparison, option B is the better financial decision.

Answer 2

A. Take $1 million now.

Step-by-step explanation:

A. If we take $1 million now the present value of the money is $1 million.

B. If we choose to take $1.2 million paid out over 3 years then present value will at 10% will be;

$300,000 + $300,000 / 1.2 + $300,000/ 1.44 + $300,000 / 1.728

$300,000 + $250,000 + $208,000+ $173,611 = $931,944

The present value of option B is less than present value of option A. We should select option A and take $1 million now.