# Lesson 16

Compounding Interest

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

### Problem 1

Automobiles start losing value, or depreciating, as soon as they leave the car dealership. Five years ago, a family purchased a new car that cost $16,490.

If the car lost 13% of its value each year, what is the value of the car now?

### Problem 2

The number of trees in a rainforest decreases each month by 0.5%. The forest currently has 2.5 billion trees.

Write an expression to represent how many trees will be left in 10 years. Then, evaluate the expression.

### Problem 3

From 2005 to 2015, a population of \(P\) lions is modeled by the equation \(P = 1,\!500 \boldcdot (0.98)^t\), where \(t\) is the number of years since 2005.

- About how many lions were there in 2005?
- Describe what is happening to the population of lions over this decade.
- About how many lions are there in 2015? Show your reasoning.

### Problem 4

A bank account pays 0.5% monthly interest.

- If $500 is put in the account, what will the balance be at the end of one year, assuming no additional deposits or withdrawals are made?
- What is the effective annual interest rate?
- Is the effective annual interest rate more or less than 6% (the nominal interest rate)?

### Problem 5

Here are the graphs of three equations: \(y = 50 \boldcdot (1.5)^x\), \(y = 50 \boldcdot 2^x\), and \(y = 50 \boldcdot (2.5)^x\).

Which equation matches each graph? Explain how you know.

### Problem 6

A major retailer has a staff of 6,400 employees for the holidays. After the holidays, they will decrease their staff by 30%.

How many employees will they have after the holidays?

### Problem 7

Ten students guessed the number of cubes in a jar that contains 202 cubes. Their names and guesses are listed in the table.

Create a scatter plot with the guesses as the horizontal values and the absolute guessing errors as the vertical values.

Andre | 205 |

Clare | 190 |

Diego | 197 |

Elena | 200 |

Han | 220 |

Jada | 210 |

Kiran | 202 |

Lin | 203 |

Mai | 199 |

Noah | 185 |