Question

lamar is considering two loans.

which loan will have the lowest total payback?

loan a will have the lowest total payback because the amount of interest paid is less than the amount of interest paid for loan b.
loan a will have the lowest total payback because the total of the principal and the interest paid for loan a is less than the same total for loan b.
loan b will have the lowest total payback because the interest is less than the interest for loan a.
loan b will have the lowest total payback because the total of the principal and the interest paid for loan b is less than the same total for loan a.

Explanation:

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<reasoning>

Calculate interest for Loan A

Using the Simple Interest Formula knowledge point
\[

$$\begin{aligned} I_A &= P_A \cdot r_A \cdot t_A \\ I_A &= 4500 \cdot 0.05 \cdot 3 \\ I_A &= 675 \end{aligned}$$

\]

Calculate total payback for Loan A

Using the Total Payback Calculation knowledge point
\[

$$\begin{aligned} A_A &= P_A + I_A \\ A_A &= 4500 + 675 \\ A_A &= 5175 \end{aligned}$$

\]

Calculate interest for Loan B

Using the Simple Interest Formula knowledge point
\[

$$\begin{aligned} I_B &= P_B \cdot r_B \cdot t_B \\ I_B &= 4300 \cdot 0.06 \cdot 3 \\ I_B &= 774 \end{aligned}$$

\]

Calculate total payback for Loan B

Using the Total Payback Calculation knowledge point
\[

$$\begin{aligned} A_B &= P_B + I_B \\ A_B &= 4300 + 774 \\ A_B &= 5074 \end{aligned}$$

\]

Compare total payback amounts

Using the Total Payback Calculation knowledge point
\[

$$\begin{aligned} 5074 &< 5175 \\ A_B &< A_A \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>Loan A will have the lowest total payback because the amount of interest paid is less than the amount of interest paid for loan B.</mcq-option>
<mcq-option>Loan A will have the lowest total payback because the total of the principal and the interest paid for loan A is less than the same total for loan B.</mcq-option>
<mcq-option>Loan B will have the lowest total payback because the interest is less than the interest for loan A.</mcq-option>
<mcq-correct>Loan B will have the lowest total payback because the total of the principal and the interest paid for loan B is less than the same total for loan A.</mcq-correct>
</answer>

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Answer:

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<reasoning>

Calculate interest for Loan A

Using the Simple Interest Formula knowledge point
\[

$$\begin{aligned} I_A &= P_A \cdot r_A \cdot t_A \\ I_A &= 4500 \cdot 0.05 \cdot 3 \\ I_A &= 675 \end{aligned}$$

\]

Calculate total payback for Loan A

Using the Total Payback Calculation knowledge point
\[

$$\begin{aligned} A_A &= P_A + I_A \\ A_A &= 4500 + 675 \\ A_A &= 5175 \end{aligned}$$

\]

Calculate interest for Loan B

Using the Simple Interest Formula knowledge point
\[

$$\begin{aligned} I_B &= P_B \cdot r_B \cdot t_B \\ I_B &= 4300 \cdot 0.06 \cdot 3 \\ I_B &= 774 \end{aligned}$$

\]

Calculate total payback for Loan B

Using the Total Payback Calculation knowledge point
\[

$$\begin{aligned} A_B &= P_B + I_B \\ A_B &= 4300 + 774 \\ A_B &= 5074 \end{aligned}$$

\]

Compare total payback amounts

Using the Total Payback Calculation knowledge point
\[

$$\begin{aligned} 5074 &< 5175 \\ A_B &< A_A \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>Loan A will have the lowest total payback because the amount of interest paid is less than the amount of interest paid for loan B.</mcq-option>
<mcq-option>Loan A will have the lowest total payback because the total of the principal and the interest paid for loan A is less than the same total for loan B.</mcq-option>
<mcq-option>Loan B will have the lowest total payback because the interest is less than the interest for loan A.</mcq-option>
<mcq-correct>Loan B will have the lowest total payback because the total of the principal and the interest paid for loan B is less than the same total for loan A.</mcq-correct>
</answer>

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