# A lottery offers two options for the prize. Option A: \$1,000 a week for life. Option B: \$600,000 in one lump sum. If you choose Option B, you have the opportunity to place the winnings into an investment that also makes regular payments, at a rate of 3%/a, compounded monthly. Which option would the winner choose if they expect to live for another 50 years? At what point in time is Option A better than Option B? Write a brief reflection about which option you would choose and why (pay attention to the math, but reflect upon how much money you would want to be spending as opposed to saving).

## Expert Answers

In many cases, when someone wins the lottery, people tend to choose the lump sum, but the assumption is that a monthly or weekly payout would be the better option.

Let's use math to prove which is actually the better of the two options.

Over 50 years, you receive \$1,000 a week, or \$1,000*(50 years)*(52 weeks/year) = \$2.6 million.

In the other scenario, you receive \$600,000 and put it into an account. You receive \$600,000*(1.0025^600) = \$2.684 million. Over that time period, you receive \$84,000 more than if you had taken the weekly benefit. Note: 1.0025 is 1 plus .03/12, the annual interest rate divided by months in the year.

To find the intersection, you need to set the equations equal to one another with the value of time (months) unknown, so 600000*(1.0025^x)=1000*(52/12)x. Simplify that to reveal that around 560 months, or nearly 47 years, it becomes more beneficial to take the lump sum. Prior to that, however, you are receiving more from the monthly benefit.

Now, if you are actually planning on using the lottery money, you will not be able to access it and earn the same amount of money if you are just investing it, so it is more practical to take the monthly benefit because you want to be able to use it for those first 47 years before it becomes more valuable to have invested it.

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