Why It Matters: Exponential and Logarithmic Functions

Why understand how exponential and logarithmic functions behave?

Many sources credit Albert Einstein as saying, “Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it.” You probably already know this if you have ever invested in an account or taken out a loan. Interest is the amount added to the balance. The beauty, in the case of investing, is that once interest is earned, it also earns interest. This idea of interest earning interest is known as compound interest. (It isn’t quite as beautiful on money you owe.)

Interest can be compounded over different time intervals.  It might be compounded annually (once per year), or more often, such as semi-annually (twice per year), quarterly (four times per year), monthly (12 times per year), weekly (52 times per year), or daily (365 times per year). There is also one more option—compounded continuously—which is the theoretical concept of adding interest in infinitesimally small increments. Although not actually possible, it provides the limit of compounding and is therefore a useful quantity in economics.

Suppose you inherit $10,000. You decide to invest in in an account paying 3% interest compounded continuously. What will the balance be in 5 years, 10 years, or even 50 years? You’ll want to know, especially for retirement planning.

In this module, you will learn about the function you can evaluate to answer these questions. You will also discover how to make changes to the variables involved, such as time or initial investment, to alter your results.