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 |