# Lesson 17

Different Compounding Intervals

### Lesson Narrative

In this lesson, students apply what they have learned about compound interest to critically examine different situations. First, they look at how credit card companies often report interest rates (nominal annual percentage rate), versus how much interest a cardholder actually pays over the course of a year on an unpaid balance (effective annual percentage rate). The effective rate is higher than the nominal rate because of the impact of compounded interest.

Next, students are asked to choose the better of two investment options with different interest rates and compounding intervals. Finally, an optional activity looks at the rising costs of college tuition and compares the rates of increase over different decades.

Throughout this lesson, students strategically write expressions, compare them, and relate them back to monetary contexts (MP2).

### Learning Goals

Teacher Facing

• Calculate the result of repeated percent increase for the same initial balance and interest rate, but compounded at different intervals.
• Compare interest rates and compounding intervals to choose the better investment option.

### Student Facing

Let's find out what happens when we repeatedly apply the same percent increase at different intervals of time.

### Student Facing

• I can calculate interest when I know the starting balance, interest rate, and compounding intervals.
• When given interest rates and compounding intervals, I can choose the better investment option.