Both here and elsewhere, I have been part of a lively and robust discussion of the role of the real-world in mathematics instruction. One concern that is often expressed of instruction that is based in real-world problems is that of time and efficiency.
But sometimes it is really easy to turn the tables and make the standard word problem the motivational setup. An example.
In my College Algebra class, I started class with the following image the other day.
And I asked What is there to wonder about here? What questions can we ask? Here is what my students came up with.
- What is APY?
- What is the difference between Rate and APY? And what does this have to do with interest?
- How much does the principal grow over time in response to the rate?
- How does the amount of the deposit affect the growth over time?
These are precisely the questions I would hope for. But they asked them, not me.
In order to get to the answer to the question about the difference between APR and APY, we have to consider this one:
If you offer a 1.54% APR, how should you go about compounding interest monthly?
I have no idea how to get my students to the place where they can ask this question, so I asked it myself. Their ideas:
- Figure a year’s worth of interest in dollars, then divide that by 12 and add to the account each month, and
- Divide the interest rate by 12. Apply this new interest rate each month.
Brilliant! Next year, I’ll use (1) as part of a homework assignment-how do we run the computations when money gets added to account midway through the year? It gets very tricky very quickly.
But (2) is how we have agreed to run the computations in the financial world.
And it’s what accounts for the difference between APR and APY.
Now they were ready to hear about and derive interest formulas and to do some computations on their own.
A small bit of preparation put my students in a much better frame of mind for the material.
Sometimes it is that easy.
But not always.