objectives
Demonstrate an understanding of compounding interest
Compare the outcomes of higher interest rates and longer periods of compounding.
time needed
30 minutes.
materials
The ability to show the video Cap Wakes Up.
An excel table showing a variety of superheroes and the dates of their first appearances.
overview
In the video clip we see Steve Rogers (aka Captain America) waking up. In an attempt to defeat a Nazi plot, he crashed a plane into the ocean where he was entombed in ice. Now, 70 years later he awakes in a world very different from the 1940s.
For Steve, this new world requires some getting used to. He may have one thing in his favor, however. During the time he was asleep, any savings he had grew, and thanks to compounding interest, he could possibly be very wealthy.
Compounding occurs when interest earned on a principle amount of money is reinvested to become part of the principle. As the principle grows, it earns more interest. As a result, interest builds more interest. Over time, this means that savings accounts can grow exponentially at a fixed interest rate.
As interest accumulates (either daily, monthly, or yearly) a deposit at the end of a time period will increase by the rate of interest. To keep the math relatively simple, let’s use an annual accumulation of interest. If interest is earned at the end of the year, then the next year the deposit is larger because interest was added to it. At the end of the second year, the new interest paid is based on the original deposit plus the first year’s interest. The growth occurs year after year based on the following equation, again assuming that the interest compounds once a year:
New Principal = (Principal) x (1+r)t
Where r = the interest rate
t = the number of time periods over which compounding occurs
For students, understanding the value of starting to save early is incredibly important. Even if they only save a small amount, the more years compounding occurs (the higher the value of t in the equation), the larger the pile of savings when it is needed.
action
Show the video Cap Wakes Up. Let students know that Steve Rogers (aka Captain America) was paid $1,000 in 1945 just before his plane crashed and that he deposited that money in a bank account paying 2% interest.
Assume that the interest on Cap’s money has been compounding ever since. Also, assume that Cap was pulled out of the ice this year (instead of the 70 years referenced in the film). Have students pair up and compute the value of the $1,000 today after the compounding.
ANSWER: Using the formula
New Principal = (Principal) x (1+r)t
Where r = the interest rate
t = the number of time periods over which compounding occurs
Substitute 0.02 in for r. The value of t will depend on what year it is. Take the current year minus 1945 to get the value of t.
Now, compute the new principle.
New Principal = ($1,000) x (1+.02)t
Maybe Cap took on a little more risk with his $1,000. Assume that instead of putting the money in the bank, Cap put his money in the stock market, and that the market has been growing at a steady rate of 7% ever since. (This is an average rate of return on stocks. The market doesn’t grow consistently, but this provides an alternative way to save.) Again, assume that Cap was pulled out of the ice this year (instead of the 70 years referenced in the film). Have students pair up and compute the value of the $1,000 today after the compounding.
Finally, using the table of superheroes and origin dates, have students individually compute the value of $1,000 for a hero of their choice. The correct answers will depend on the interest rate and the value of t.
discussion
Ask students about their observations. Specifically, ask them about the two ways a fixed sum of money can grow over time. They should understand by this point that a larger interest rate, and a longer amount of time can work in a saver’s favor.
As a final point of emphasis, show them the comic panel of Cable talking to a group of low-level superheroes looking for business funding. Since Cable can travel through time, he never has to worry about money. Why? Because he understands the power of compounding!
Here are some wrap up questions:
NOTE: If you have a Kahoot! account, there is a link to a Kahoot! using the following questions below.
1. If Captain Marvel wants to retire from hero work when she is 60 years old, she should start saving
a. when she turns 60.
b. as soon as possible.
c. never because superheroes has a great pension plan.
d. when she has enough income to be comfortable.
Answer: (b) As soon as possible. If she waits until closer to retirement then she would have to save a huge portion of her income. If she waits until she has enough income to be comfortable she may never start saving.
2. Deadpool has been saving to open his new business. After checking in with his accountant he finds that despite saving $1,000,000 he still can’t afford to start operations. What might have happened while he was saving money?
a. One of his enemies has stolen his savings.
b. Deadpool has an unethical money manager.
c. Deadpool secretly took money out of his savings account.
d. All of the above.
Answer: (d) One of the key aspects of compounding is that you need to leave the money in the account. If someone steals money from his account, be it an enemy, the money manager, or Deadpool himself, the principle will not be as large as it was so the compounding doesn’t work as well.
NOTE: If you talk about how inflation erodes the purchasing power of money, you could replace option b above with “Inflation reduced the purchasing power of his savings”.
3. Cable has gone back in time to put some money away so that he will have some in the present. What would affect how much he earns over time?
a. The interest rate
b. The name of the bank where he made his deposit
c. The name he used for his account.
d. How far back in time he went.
Answer: (a) and (d) The two main things that affect how much money he has would be the interest rate and the number of years the interest compounds. Higher interest rates lead to a faster accumulation of interest, while more time allows the interest to compound more times. Both of these will lead to greater gains.
4. Oliver Queen (the Green Arrow) has been lost at sea for years. Over this time his $100 million trust fund has been accumulating interest at a rate of 12%. If when he returns, he finds that he now has $200 million in his account, how long was he gone?
a. 16.7 years
b. 5 years
c. 6 years
d. It is impossible to know.
Answer: (c) Using the law of 72 you need to solve for the number of years it would take Ollie’s trust fund to double. 72 divided by the rate of interest will give you the answer.
72/12 = 6. This means that Ollie was gone for six years.
