Compounding Interest

ID: jonuf-luzan
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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.

A template for answering this question. Ask your instructor for an alternative.

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.

A template for answering this question. Ask your instructor for an alternative.