To determine the interest rate at which the bank makes the most money and takes the most risk, we need to look at the total amount paid for each interest rate over the five-year period for a [tex]$10,000 loan. Here's the information given in the table:
\[
\begin{array}{|c|c|c|}
\hline
\text{Interest rate} & \text{Monthly payment} & \text{Total paid} \\
\hline
5 \% & \$[/tex]188.70 & \[tex]$11,322.00 \\
\hline
10 \% & \$[/tex]212.50 & \[tex]$12,750.00 \\
\hline
15 \% & \$[/tex]237.90 & \[tex]$14,274.00 \\
\hline
18 \% & \$[/tex]253.90 & \[tex]$15,234.00 \\
\hline
\end{array}
\]
Step-by-Step Solution:
1. Identify the Total Paid Amounts: We have four different total paid amounts associated with each interest rate:
- At 5%, the total paid is \$[/tex]11,322.00.
- At 10%, the total paid is \[tex]$12,750.00.
- At 15%, the total paid is \$[/tex]14,274.00.
- At 18%, the total paid is \[tex]$15,234.00.
2. Determine the Highest Total Paid: Among the total paid amounts, we need to determine which is the highest. Let's list them and identify the maximum:
- \$[/tex]11,322.00 (5%)
- \[tex]$12,750.00 (10%)
- \$[/tex]14,274.00 (15%)
- \[tex]$15,234.00 (18%)
The highest total paid amount is \$[/tex]15,234.00.
3. Identify the Corresponding Interest Rate: The total paid amount of \$15,234.00 corresponds to an interest rate of 18%.
Therefore, the bank makes the most money and takes the most risk with an interest rate of 18 percent.
