## IN THE LIMIT-CONTINUOUS COMPOUNDING

This section just shows a point that is probably interesting for those comfortable with the math. It’s not a necessary section. However, I recommend looking at the graph and reading through the description of the axes.

The balance of a loan that’s compounded once a year at, say, 10% annual interest grows by 10% a year. As I have shown above, if the same loan is compounded monthly (12 times a year), the balance grows by 10.47% a year. What if the loan is compounded more often—weekly, daily, or even hourly? Does the effective interest rate just keep growing?

1 10 100 1,000 10,000

Number of compounding intervals per year Figure 2.1 Effective interest rate versus the number of compounding intervals per year.

The answer to this question is shown in Figure 2.1...

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