- Calculate the total interest earned for each rate: \(\$1,322.00\) at \(5\%\), \(\$2,750.00\) at \(10\%\), \(\$4,274.00\) at \(15\%\), and \(\$5,234.00\) at \(18\%\).
- Recognize that the total interest earned increases directly with the interest rate.
- Relate higher interest rates to the financial principle that higher risk requires higher potential reward for the lender.
- Identify that the \(18\%\) rate provides the highest profit and corresponds to the highest risk.
- Final Answer: \(\boxed{18}\) percent.
Explanation
- Data and Problem Analysis
To determine which interest rate results in the highest earnings and the greatest risk for the bank, we start by analyzing the provided data for a \$10,000 loan over a five-year period. The bank's profit from a loan is the total amount paid by the borrower minus the original principal, which is \$10,000. Higher total payments directly correspond to higher interest earnings for the bank. Furthermore, financial institutions typically assign higher interest rates to loans that carry a higher risk of default, meaning the highest interest rate also corresponds to the highest risk level.
- Calculating Interest Earnings
We calculate the total interest earned by the bank for each interest rate using the formula: \(\text{Total Interest} = \text{Total Paid} - \text{Principal}\).
- For an interest rate of \(5\%\): \(\$11,322.00 - \$10,000 = \$1,322.00\).
- For an interest rate of \(10\%\): \(\$12,750.00 - \$10,000 = \$2,750.00\).
- For an interest rate of \(15\%\): \(\$14,274.00 - \$10,000 = \$4,274.00\).
- For an interest rate of \(18\%\): \(\$15,234.00 - \$10,000 = \$5,234.00\).
- Comparing Earnings and Risk Conclusion
By comparing the interest earnings calculated for each rate, we can clearly see the trend: as the interest rate increases, the total interest earned by the bank also increases. The highest interest amount, \(\$5,234.00\), is generated by the \(18\%\) interest rate. As stated, higher interest rates serve to compensate the bank for higher risks, such as the increased possibility that the borrower may not be able to repay the loan. Therefore, the \(18\%\) interest rate is associated with both the highest profit and the highest risk for the bank. The correct choice is 18 percent.
Examples
When you apply for a credit card or a loan, the interest rate you are offered often depends on your credit history. If a bank perceives a borrower as high-risk, they might approve the loan but at a much higher interest rate to ensure they are adequately compensated for that risk. Conversely, a borrower with an excellent credit score is seen as lower risk and is often offered a lower interest rate, which is a practical application of the balance between risk and return in finance. Understanding these calculations helps in making informed decisions about borrowing money and managing personal debt.