Question

a photographer takes out a simple interest loan to purchase a \\$1,600 camera at 2\\% interest rate. use the function \\(i = prt\\) to interpret the rate of the change for the interest, \\(i\\), charged per year, \\(t\\).

• the photographer will have to pay interest for 32 months.
• the photographer will have to pay \\$3,200 of interest for every year of the loan repayment.
• the photographer will have to pay interest for 3,200 months.
• the photographer will have to pay \\$32 of interest for every year of the loan repayment.

Explanation:

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<reasoning>

Identify the given values

We are given:

• Principal amount \(p = \$1,600\)
• Annual interest rate \(r = 2\% = 0.02\)
• Simple interest formula \(I = prt\)
• Time \(t\) is measured in years.

Calculate the rate of change

The rate of change of interest \(I\) with respect to time \(t\) is the derivative \(\frac{dI}{dt}\) or the coefficient of \(t\) in the linear equation:
\[
\text{Rate of change} = pr
\]
Substituting the given values:
\[
pr = 1600 \times 0.02 = 32
\]

Interpret the rate of change

The rate of change is \(32\) dollars per year. This means that the photographer will have to pay \(\$32\) of interest for every year of the loan repayment.

Match with the options

Let's evaluate the given choices:

• Option 1: "The photographer will have to pay interest for 32 months." (Incorrect)
• Option 2: "The photographer will have to pay \$3,200 of interest for every year of the loan repayment." (Incorrect)
• Option 3: "The photographer will have to pay interest for 3,200 months." (Incorrect)
• Option 4: "The photographer will have to pay \$32 of interest for every year of the loan repayment." (Correct)

</reasoning>

<answer>
<mcq-option>The photographer will have to pay interest for 32 months.</mcq-option>
<mcq-option>The photographer will have to pay $3,200 of interest for every year of the loan repayment.</mcq-option>
<mcq-option>The photographer will have to pay interest for 3,200 months.</mcq-option>
<mcq-correct>The photographer will have to pay $32 of interest for every year of the loan repayment.</mcq-correct>
</answer>

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"Simple Interest"
]
}
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Answer:

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<reasoning>

Identify the given values

We are given:

• Principal amount \(p = \$1,600\)
• Annual interest rate \(r = 2\% = 0.02\)
• Simple interest formula \(I = prt\)
• Time \(t\) is measured in years.

Calculate the rate of change

The rate of change of interest \(I\) with respect to time \(t\) is the derivative \(\frac{dI}{dt}\) or the coefficient of \(t\) in the linear equation:
\[
\text{Rate of change} = pr
\]
Substituting the given values:
\[
pr = 1600 \times 0.02 = 32
\]

Interpret the rate of change

The rate of change is \(32\) dollars per year. This means that the photographer will have to pay \(\$32\) of interest for every year of the loan repayment.

Match with the options

Let's evaluate the given choices:

• Option 1: "The photographer will have to pay interest for 32 months." (Incorrect)
• Option 2: "The photographer will have to pay \$3,200 of interest for every year of the loan repayment." (Incorrect)
• Option 3: "The photographer will have to pay interest for 3,200 months." (Incorrect)
• Option 4: "The photographer will have to pay \$32 of interest for every year of the loan repayment." (Correct)

</reasoning>

<answer>
<mcq-option>The photographer will have to pay interest for 32 months.</mcq-option>
<mcq-option>The photographer will have to pay $3,200 of interest for every year of the loan repayment.</mcq-option>
<mcq-option>The photographer will have to pay interest for 3,200 months.</mcq-option>
<mcq-correct>The photographer will have to pay $32 of interest for every year of the loan repayment.</mcq-correct>
</answer>

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