To determine the interest rate at which banks make the most money and take the most risk, we need to carefully analyze the given data. Let's break down the information step-by-step:
### Step 1: Understanding the Data
We are given a table displaying the interest rates and corresponding monthly payments along with the total paid over five years for a [tex]$10,000 loan. The table is as follows:
| Interest rate | Monthly payment | Total paid |
|---------------|-----------------|-------------|
| 5% | $[/tex]188.70 | [tex]$11,322.00 |
| 10% | $[/tex]212.50 | [tex]$12,750.00 |
| 15% | $[/tex]237.90 | [tex]$14,274.00 |
| 18% | $[/tex]253.90 | [tex]$15,234.00 |
### Step 2: Determine Where Banks Make the Most Money
To identify the interest rate at which banks make the most money, we look at the "Total paid" column. We are interested in finding the highest total paid amount as this indicates where the bank makes the most money.
Here are the total paid values:
- At 5% interest rate, total paid = $[/tex]11,322.00
- At 10% interest rate, total paid = [tex]$12,750.00
- At 15% interest rate, total paid = $[/tex]14,274.00
- At 18% interest rate, total paid = [tex]$15,234.00
The highest total paid amount is $[/tex]15,234.00 which corresponds to the 18% interest rate. Therefore, banks make the most money with an 18% interest rate.
### Step 3: Determine Where Banks Take the Most Risk
Typically, the higher the interest rate, the higher the risk involved for the lender. This is because higher interest rates can lead to an increased likelihood of borrower default. Hence, the interest rate that represents the most risk for the banks is the highest interest rate listed in the table.
The interest rates given are:
- 5%
- 10%
- 15%
- 18%
The highest interest rate here is 18%. Therefore, banks take the most risk with an 18% interest rate.
### Conclusion
After analyzing the table, we can conclude that:
- Banks make the most money with an 18% interest rate.
- Banks take the most risk with an 18% interest rate.
Thus, the answer is:
Banks make the most money and take the most risk with an interest rate of 18 percent.
