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

AI-F.LE.1

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

AI-F.LE.1a

Justify that a function is linear because it grows by equal differences over equal intervals, and that a function is exponential because it grows by equal factors over equal intervals.

AI-F.LE.1b

Recognize situations in which one quantity changes at a constant rate per unit interval relative to another, and therefore can be modeled linearly.

AI-F.LE.1c

Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another, and therefore can be modeled exponentially.

AI-F.LE.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.

Investigation: Comparisons of simple and compound interest

Objective

Vocabulary

Discussion questions