# Lesson 16

Compounding Interest

### Lesson Narrative

In this lesson, students continue to examine repeated percent change and practice representing it with expressions. An important focus of the lesson is on distinguishing the effect of compounded percent change from that of simple percent change.

Students begin exploring this distinction geometrically by contrasting the outcome of scaling up the length of an image by 10% twice, versus scaling up the length by 20% once. They turn to a financial context next. Students investigate the effect on a savings account balance of calculating 1% interest every month for a year versus 12% once. In both cases, they see that the repeated application of a percent change yields a greater final change because, with each iteration, the value that is used to compute the percent increase grows. They learn that this process is called compounding.

Students critically examine the two ways of scaling an image and make a reasoned argument about whether the two results are equal (MP3). Students also look for equations to represent repeated interest calculations in the second activity (MP8).

### Learning Goals

Teacher Facing

• Compare the outcome of applying a percent increase, $p$, $n$ times to the outcome of applying the percent increase $np$.
• Justify (orally and in writing) why applying a percent increase $p$, $n$ times, is not equivalent to applying the percent $np$.

### Student Facing

Let's explore different ways of repeatedly applying a percent increase.

### Student Facing

• I can explain why applying a percent increase, $p$, $n$ times is like or unlike applying the percent increase $np$.