I use the following video clip from Seinfeld to teach about the time value of money.
The clip can be found here:
I show the first 1:51 minutes of the clip and ask “What’s the value of $50 (not) received 53 years ago? The interest rate is 5%.”
The answer, of course, is FV = $50 * 1.0553 = $663.75
I revisit the same clip when I talk about the difference between annual percentage rates and effective annual rates. The question now becomes “What’s the value of $50 (not) received 53 years ago? The interest rate is 5%, quarterly compounded.”
I then ask my students how they interpret the 5%: is it an APR or an EAR? Depending on the assumption, you get different results:
- Annual compounding (original question)
- FV = 50 * 1.0553 = 663.75
- Quarterly compounding if 5% is an EAR
- Quarterly rate r: (1+r)4 = 1.05 <=> r = 1.22722%
- FV = 50 * 1.0122722(53*4) = 663.75
- Quarterly compounding if 5% is an APR
- Period rate r = 5%/4 = 1.25%
- FV = 50 * 1.0125(53*4) = 696.17
Since interpreting it as an EAR gives the same result as annual compounding, it only makes sense to interpret it as an APR (why would you mention quarterly compounding otherwise?).
I then show the clip from minute 1:51 to 2:13. It looks like the Hollywood screenwriters were right about the future value or about the compounding, but not both. The life lesson here is: Don’t rely on Hollywood script writers for financial advice.