To determine which interest rate makes the bank the most money from a \[tex]$10,000 loan over five years, we need to evaluate the total payments made under each interest rate and compare them.
Given the total payments for each interest rate:
- For 5%: \$[/tex]11,322.00
- For 10%: \[tex]$12,750.00
- For 15%: \$[/tex]14,274.00
- For 18%: \[tex]$15,234.00
First, we calculate the difference between the total amount paid and the principal amount (which is \$[/tex]10,000) to find the interest amount paid at each rate.
1. For 5% interest rate:
- Total paid: \[tex]$11,322.00
- Difference (interest amount): \$[/tex]11,322.00 - \[tex]$10,000 = \$[/tex]1,322.00
2. For 10% interest rate:
- Total paid: \[tex]$12,750.00
- Difference (interest amount): \$[/tex]12,750.00 - \[tex]$10,000 = \$[/tex]2,750.00
3. For 15% interest rate:
- Total paid: \[tex]$14,274.00
- Difference (interest amount): \$[/tex]14,274.00 - \[tex]$10,000 = \$[/tex]4,274.00
4. For 18% interest rate:
- Total paid: \[tex]$15,234.00
- Difference (interest amount): \$[/tex]15,234.00 - \[tex]$10,000 = \$[/tex]5,234.00
Now, we compare these differences to determine which interest rate results in the highest interest amount paid, which also indicates the most profit for the bank.
- Interest amount at 5%: \[tex]$1,322.00
- Interest amount at 10%: \$[/tex]2,750.00
- Interest amount at 15%: \[tex]$4,274.00
- Interest amount at 18%: \$[/tex]5,234.00
The highest interest amount paid is \$5,234.00, which corresponds to the 18% interest rate. Therefore, the interest rate that makes the bank the most money is 18 percent.
