5. Olivia Kelly has just won the Beawinner Lottery and can elect one of two options for her payments. She can either receive $500,000 today or she can receive three annual payments as follows: $100,000 at the end of the first year, $200,000 at the end of the second year, and $300,000 at the end of the third year. If she believes she can make an investment that will pay a 9% compounded annually interest rate, should she take the $500,000 or the three payments?

It is better to receive the $500,000 now.

Explanation:

Giving the following information:

Option 1:

Receive $500,000 today.

Option 2:

Three annual payments of $100,000, $200,000 and $300,000 at the end of each year.

Annual interest of 9%.

There are two different ways of determining which option is the best. We can calculate the present value of the three payments and compare them to $500,000, or calculate the final value at an interest rate of 9% compounded annually.

Present value:

PV = FV / (1+i) ^n

The present value of the second option:

PV = 300,000/1.09^3 + 200,000/1.09^2 + 100,000/1.09 = $491,734.17

Final value:

FV = PV * (1+i) ^n

Option 1:

FV = 500,000 * (1.09) ^3 = $647,514.5

Option 2:

FV = 100,000*1.09^2 + 200,000*1.09 + 300,000 = $636,810

In both ways, option 1 is better.