# Investigation: Comparisons of simple and compound interest

Lesson

### Objective

Compare simple interest and compound interest

### Vocabulary

Define each of the terms below.  Be sure to use these terms when discussing the activity below with your classmates.

• Interest:
• Simple interest:
• Compound interest:
• Interest rate:

#### Discussion questions

The two tables below demonstrate how to calculate simple interest and compound interest.  Complete the tables to determine the total interest earned and the ending balance after five-years, with an initial deposit of $100. Simple Interest Year Amount to Earn Interest Interest Rate Interest Earned Ending Balance 1$100 5% (100)x(.05) = $5.00$100
2 $100 5% 3 5% 4 5% 5 5% Total Compound interest (truncate after the hundredths place Year Amount to Earn Interest Interest Rate Interest Earned Ending Balance 1$100 5% (100)x(.05)=$5.00$105
2 \$105 5%
3   5%
4   5%
5   5%
Total

In words write a comparison of simple interest and compound interest, then discuss your reasoning with a partner (using the tables you completed and the vocabulary terms listed above).

### Outcomes

#### F.LE.A.1

Distinguish between situations that can be modeled with linear functions and with exponential functions.

#### F.LE.A.1.A

Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

#### F.LE.A.1.B

Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

#### F.LE.A.1.C

Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

#### F.LE.A.3'

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 'Linear and exponential