Sure! Let's carefully match each definition or formula to the correct interest type: simple interest or compound interest.
### Definitions and Formulas:
1. Formula: [tex]\( A = P \left(1 + \frac{r}{n} \right)^{nt} \)[/tex]
2. Definition: Interest calculated once
3. Definition: Interest calculated multiple on the starting principal times over the course of a loan
4. Formula: Total Interest = Principal × APR (as a decimal) × Term of Loan
### Matching Process:
- Simple Interest:
- Simple interest is described as "Interest calculated once."
- The formula related to simple interest is:
[tex]\[
\text{Total Interest} = \text{Principal} \times \text{APR} \times \text{Term of Loan}
\][/tex]
- Compound Interest:
- Compound interest is defined as "Interest calculated multiple on the starting principal times over the course of a loan."
- The formula related to compound interest is:
[tex]\[
A = P \left(1 + \frac{r}{n} \right)^{nt}
\][/tex]
### Final Matching in a Table:
Based on the above definitions and formulas, we can represent the matching as follows:
[tex]\[
\begin{array}{|l|l|}
\hline \text{Simple Interest} & \text{Compound Interest} \\
\hline
\text{Interest calculated once} & \text{Interest calculated multiple on the starting principal times over the course of a loan} \\
\text{Total Interest} = \text{Principal} \times \text{APR (as a decimal)} \times \text{Term of Loan} & A = P \left(1 + \frac{r}{n} \right)^{nt} \\
\hline
\end{array}
\][/tex]
So, matching each definition or formula to the correct interest type, we have:
Simple Interest:
- Interest calculated once
- Total Interest = Principal × APR (as a decimal) × Term of Loan
Compound Interest:
- Interest calculated multiple on the starting principal times over the course of a loan
- [tex]\( A = P \left(1 + \frac{r}{n} \right)^{nt} \)[/tex]
