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.

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