Compounding Interest

ID: jonuf-luzan
Created by Illustrative MathematicsIllustrative Mathematics, CC BY 4.0
Subject: Algebra, Algebra 2
Grade: 8-9
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16 questions

Compounding Interest

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Problem 1

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?

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Problem 2

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

2) Write an expression to represent how many trees will be left in 10 years.

3) Evaluate the expression.

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Problem 3

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

4) About how many lions were there in 2005?

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5) Describe what is happening to the population of lions over this decade.

6) About how many lions are there in 2015?

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7) Show your reasoning.

Problem 4

A bank account pays 0.5% monthly interest.

8) 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?

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9) What is the effective annual interest rate?

10) 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(1.5)xy = 50 \cdot (1.5)^x​​, y=502xy = 50 \cdot 2^x, and y=50(2.5)xy = 50 \cdot (2.5)^x.

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Here are the graphs of three equations.

Which graph matches each of the equations below? Write the letter of the correct graph in the answer box.

11) y=50(1.5)xy = 50 \cdot (1.5)^x

12) y=502xy = 50 \cdot 2^x

13) y=50(2.5)xy = 50 \cdot (2.5)^x

14) Explain how you know.

Problem 6

15) 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?

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Problem 7

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

StudentGuessAndre205Clare190Diego197Elena200Han220Jada210Kiran202Lin203Mai199Noah185\begin{array}{|c|c|} \hline \\[-1em] \textbf{Student} & \textbf{Guess} \\[-1em] \\ \hline \\[-1em] \text{Andre} & 205 \\[-1em] \\ \hline \\[-1em] \text{Clare} & 190 \\[-1em] \\ \hline \\[-1em] \text{Diego} & 197 \\[-1em] \\ \hline \\[-1em] \text{Elena} & 200 \\[-1em] \\ \hline \\[-1em] \text{Han} & 220 \\[-1em] \\ \hline \\[-1em] \text{Jada} & 210 \\[-1em] \\ \hline \\[-1em] \text{Kiran} & 202 \\[-1em] \\ \hline \\[-1em] \text{Lin} & 203 \\[-1em] \\ \hline \\[-1em] \text{Mai} & 199 \\[-1em] \\ \hline \\[-1em] \text{Noah} & 185 \\[-1em] \\ \hline \end{array}

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

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