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Sagot :
Let's categorize the given definitions and formulas for simple and compound interest correctly.
### Simple Interest
1. Formula:
[tex]\[ \text{Total Interest} = \text{Principal} \times \text{APR (as a decimal)} \times \text{Term of Loan} \][/tex]
2. Definition:
Interest calculated once on the starting principal.
### Compound Interest
1. Formula:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{ nt } \][/tex]
2. Definition:
Interest calculated multiple times over the course of a loan.
Now, let's organize this information on the table to indicate the correct categories:
[tex]\[ \begin{tabular}{|c|c|} \hline \textbf{Simple Interest} & \textbf{Compound Interest} \\ \hline \text{Interest calculated once on the starting principal} & \text{Interest calculated multiple times over the course of a loan} \\ \hline \text{Total Interest = Principal $\times$ APR (as a decimal) $\times$ Term of Loan} & \text{A = P $\left(1+\frac{r}{n}\right)^{ nt }$} \\ \hline \end{tabular} \][/tex]
Here, the correct matching has been provided for simple and compound interest definitions and formulas.
### Simple Interest
1. Formula:
[tex]\[ \text{Total Interest} = \text{Principal} \times \text{APR (as a decimal)} \times \text{Term of Loan} \][/tex]
2. Definition:
Interest calculated once on the starting principal.
### Compound Interest
1. Formula:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{ nt } \][/tex]
2. Definition:
Interest calculated multiple times over the course of a loan.
Now, let's organize this information on the table to indicate the correct categories:
[tex]\[ \begin{tabular}{|c|c|} \hline \textbf{Simple Interest} & \textbf{Compound Interest} \\ \hline \text{Interest calculated once on the starting principal} & \text{Interest calculated multiple times over the course of a loan} \\ \hline \text{Total Interest = Principal $\times$ APR (as a decimal) $\times$ Term of Loan} & \text{A = P $\left(1+\frac{r}{n}\right)^{ nt }$} \\ \hline \end{tabular} \][/tex]
Here, the correct matching has been provided for simple and compound interest definitions and formulas.
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