# (Econ - Med) We've got just what need!

You and your significant other are pregnant with your first child. You’ve heard about the momentous costs of raising a kid, and you know college will only get more expensive. But more so, you want to leave a legacy. You want to make sure that your kid, to some basic degree, will always be taken care of.

So you take your concerns to your local insurance agent, and he responds “well sir (or madame), we actually have just the product for you!” And from there, he introduces you to the “ANNUITY” --- an investment product you can purchase today that guarantees you payment of a specific amount of money every month for a specified period of time…

He narrows the options down to 2 choices for you:

• THE ANNUITY: $500/month paid out to your child from birth until 30 years of age. • THE PERPETUITY:$350/month paid to your child FOREVER…. (basically an annuity, but paid perpetually)

Both are priced exactly the same. You figure a decent investment rate of return (and hence discount rate) will always be around 6% annually. So speaking strictly in terms of “economic value,” which is the better buy? Which one should you pick?

BACKGROUND / HINT: So we’ve explored the concept of calculating the Future Value (FV) of a specified stream of constant payments, as well as the Present Value (PV) of a future payment. But now were taking it a bit further… If you need a REFRESHER, click the links above. But if you want a HINT, CLICK HERE!

Part of the puzzle (of life) is uncovering implicit clues, while deciding what assumptions to make. So comment on any ambiguities you see so others can learn to spot them too!

# (Physics - Easy) Fire the Rockets!

(Original question contributed by Professor Autar Kaw; modified under permission of CCL 4.0)

Have you ever wanted to be the smartest person there is? Well then, you may want to be a rocket scientist!

You a running rocketry test using a miniature prototype. Through many measurements you figure out an equation that describes the distance covered in meters by the rocket in its current configuration:

Using this information, figure out what the acceleration of the rocket is at t=2.

Part of the puzzle (of life) is uncovering implicit clues, while deciding what assumptions to make. So comment on any ambiguities you see so others can learn to spot them too!

# (Probability - Medium) Call His Bluff

It's poker night and the game is Texas Holdem. Now, get your poker face on and crunch those numbers!

You're sitting in the final round of betting with pocket rockets (a pair of Aces) in your hand. On the table there is an 8 of diamonds, 2 of hearts, 3 of spades, 4 of clubs, and the dealer just revealed a 6 of clubs. Two of your opponents just folded, and one is betting as if he had a 5 to complete the straight on the table.

What is the probability that your opponent has a 5 in his hand?
Here's a refresher on Texas Holdem

Part of the puzzle (of life) is uncovering implicit clues, while deciding what assumptions to make. So comment on any ambiguities you see so others can learn to spot them too!

# (Geometry - Medium) Designing a Tent

For your next project, you decide to design and build your own backpacking tent. You've sketched out a side-view cross-section of the tent below. The remaining dimensions you need to figure out is the peak vertical height of the tent (for the tent poles), and where the peak height is located - the length below - relative to a corner of the tent.

What are the dimensions of the length and height above?

Part of the puzzle (of life) is uncovering implicit clues, while deciding what assumptions to make. So comment on any ambiguities you see so others can learn to spot them too!

# (Math - Easy) Plotting Lines for Robots

You're programming the static path for a robot in an enclosed room. The room is represented by a grid with the starting point at the origin (0,0).

After the robot reaches the point (2, -3) represented by the grid, you want it to travel a path perpendicular to another line y = 5x - 13 to avoid crashing into a table.

What's the equation of the line your robot needs to know?