#### Decision #5

If *you* won the lottery, which do you think you would take… and why?

At the beginning of this lesson, we asked you to consider which cash option you would take if you won the lottery. Would you take a lump-sum cash payout now or 26 equal payments over 25 years? This is actually a hard question to answer before you have all the facts, so let us give you some key things to note about the real lottery and the lottery as we are depicting it.

Imagine yourself as the sole winner of a $10 million MEGA MILLIONS jackpot. If this
were to happen to you in real life, be aware that there would be tax obligations;
however, because we're only *pretending* to win the lottery, we will also
*pretend* there are no tax obligations.

If you were to choose the annuity option, you would receive an initial payment of $384,615.38, followed by 25 more payments of the same amount. That's a nice paycheck to receive each year. After 25 years, you will have received the entire $10,000,000 and not a penny more.

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We can analyze the life of our lottery payments by looking at it in terms of pizza. We'll assume we are going to have 3 percent inflation for the next 25 years. As you can see, you'll pay more than twice as much for a slice of pizza 25 years from now as you will today. What does this mean in terms of the lottery?

Well, if we spent two of our lottery payments on pizza—specifically, the first and last—let's see how that would look:

It's clear you get much less for the same amount of money twenty five years from now, thus showing that the first lottery payment has a lot more buying power than the last.

Unfortunately, the lottery managers will not increase your payments over the years
to compensate you for your loss of purchasing power. You won 10 million and,
*this is important*, they want you to have accumulated the entire 10 million,
*25 years from now* and not one cent more.

Let's put together everything you've learned in this course and think about that last statement:

*The lottery managers want you to have accumulated the entire 10 million,*

**25 years from now.**The question is, why? To answer this, we have to consider the lump-sum payout option.

You've seen what happens to the buying power of annual payments. So, you consider the cash payout. After all, why should you accept annual payments that will buy you less and less stuff each year? Therefore, it may seem that the cash payout is the better choice.

Because you won $10,000,000, and in our pretend world there are no taxes, you think
the payout will be $10,000,000. If the lottery gives you $10,000,000, you could
put it in savings for 25 years, earning 3 percent interest each year, giving
you $18,061,112 in 25 years. The lottery didn't promise you 18 million, nor the
time to turn what they did promise into 18 million. The promise was 10 million.
Remember, they want you to have accumulated the entire 10 million *in 25 years*.

To say this another way, when you win 10 million dollars from the lottery, you are
winning the value of 10 million dollars 25 years from now. And, as you know,
10 million dollars 25 years from now is NOT the same as 10 million dollars today.
Therefore, the lottery managers are going to give you *today* the equivalent
of 10 million dollars *25 years from now! Aw, man! *

Knowing all that, consider the following question.

*If the lottery will pay you 10 million dollars 25 years from now (but 26 payments!), how much money would they have to give you today to equal this in value, assuming a 3% inflation rate?*

Using the calculator, choose the correct formula for this problem, replace the variables with the correct values and then answer the question below.

That's incorrect. If this is the answer you received, you used the future value formula instead of the present value formula. The equation you solved was:

FV=10,000,000[(1+.03)^{26}]

The equation you should have solved was:

PV=10,000,000[1/(1+.03)^{26}]

That's incorrect. If this is the answer you received, you used the correct formula, but you calculated for 25 payments instead of 26. Even though you get the money 25 years from now, you have to calculate present value based on number of payments. The equation you solved was:

PV=10,000,000[(1+.03)^{25}]

The equation you should have solved was:

PV=10,000,000[1/(1+.03)^{26}]

That's incorrect. If this is the answer you received, you used the future value formula instead of the present value formula AND you calculated the formula based on 25 years instead of 26 payments. The equation you solved was:

FV=10,000,000 [(1+.03)^{25}]

The equation you should have solved was:

PV=10,000,000[1/(1+.03)^{26}]

That's correct! If this is the answer you received, you used the correct formula, and you calculated for the correct number of payments. Good job!

You want to know what the present value of 10 million dollars is because the lottery is promising you the value of 10 million dollars 25 years (but 26 payments) from now. Having worked through this application of present value, you will know exactly what to expect when you win the lottery (or when your friends want to borrow money!).