# (Economics) From Home-Renter to Home-Owner!

You’ve done it. You’ve finally decided to buy a house… sometime in the next 5 years. You’ve got your eye on a certain neighborhood. The homes aren’t any “mansion-in-the-sky.” But it doesn’t matter. Because baby, it’s all yours… (Cough! Well actually it’s the bank’s... at least till you pay it off. But who likes that dream?)

But now that you’ve decided to buy in 5 years, you realize you need to start saving. You figure if home prices continue their uptrend, you’re dream house will probably cost about 325,000 USD once you’re ready. The average cash down-payment typically runs about 20% of the purchase price. And for the foreseeable future, it seems reasonable that you can get 7% annual return (compounded monthly) if you invest your savings in a mutual fund.

If you choose to automatically deposit money every month into such a fund, how much do you need to save each month in order to afford the down-payment for this house?

FOUNDATIONAL TOOL / HINT: So this is a jump off a cash-flow concept we’ve explored in the past… but this time, from a different angle. If you haven’t explored this or need a refresher, CLICK HERE to revisit the explanation. But if you just need a simple Hint, then CLICK HERE

# (Thermo) Energy In & Out Of A Stirling Engine

You've just gotten your hands on a stirling engine (Dean Kamen thinks these things could power the world). The engine takes an input from a heat source and outputs work.

In this case, a pressure sensor tells us that the heat source compresses the (ideal) gas inside the piston chamber from 200 kPa to 300 kPa. As a result of the process, the internal energy of the gas increases by 10 kJ, and 140 kJ of heat is transferred to the surroundings.

How much work was done by the gas during this part of the process?

# (Calculus) Angle Between Two Vectors

The angle in  degrees between two vectors

and

most nearly is

(Original question contributed by Professor Autar Kaw. Modified with permission.)

# (Physics) Relative Speed of an Elastic Collision

Two balls that are dropped from a height hi above the ground, one on top of the other. Ball 1 is on top and has mass m1, and ball 2 is undernearth and has mass m2 with m2 >> m1. Ball 2 first collides with the ground and rebounds with speed v0. Then as ball 2 starts to move upward, it collides elastically with the ball 1 which is still moving downwards also with speed v0. The final speed of ball 1 relative to ball 2 after they collide is...

# (Economics) Today, You're LeBron James...

Just for today, let’s pretend that you are Lebron James. This is it, the day you announce to the world that you’re finally returning home to the Cleveland Cavaliers.  But before you can, you need to accept one of Cleveland’s 2 tempting salary offers;

• OFFER #1: $21 Million per year, for 2 years (paid at end of each year). • OFFER #2:$44 Million as a single “lump-sum,” at the end of 2 years.

You know that you’d always rather get your money quicker. But Offer #1 is less money total… And even though Offer #2 seems like more, you have to wait longer. And there’s always a “time-value” for money…

If it's reasonably-assured you'll make 6% (per year) in the market over the next 2 years... strictly “economically-speaking,” which future offer is worth more today?

[FOUNDATIONAL TOOL: The notion of “Present Value” in “The Power of Compound Interest (Econ Pt 1 of 2)”. ----> Previously, we explored how to calculate the “Future Value” of a sum of money you have today. But now we're switching gears and asking you to do the opposite: Calculate the Present Value of a sum of money you’ll receive in the future instead. If you need a refresher of how Future Value relates to Present Value, click here!]