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Read the table that displays interest and total payments on a loan.



\begin{table}

\captionsetup{labelformat=empty}

\caption{Interest and Total Payments $\$ 10,000$ Loan over Five Years}


Interest rate		Monthly paymentTotal paid

5\%		\$188.70\$11,322.00

10\%		\$212.50\$12,750.00

15\%		\$237.90\$14,274.00

18\%		\$253.90\$15,234.00




\end{table}



Banks make the most money and take the most risk with an interest rate of

A5 percent.
B10 percent.
C15 percent.
D18 percent.

Verified Answer :

  • Define the bank's profit as the difference between the total paid and the principal (\$10,000).
  • Calculate the profit for each interest rate: 5% (\(\$1,322\)), 10% (\(\$2,750\)), 15% (\(\$4,274\)), and 18% (\(\$5,234\)).
  • Identify the 18% interest rate as the one yielding the highest profit of \(\$5,234\).
  • Recognize that the 18% rate also corresponds to the highest risk level.
  • Final answer: \(\boxed{18}\) percent.

Explanation

  1. Analysis of Loan Data and Risk

The goal is to determine which interest rate leads to the highest profit for the bank and the highest risk exposure, based on a \$10,000 loan over five years. We are provided with the "Total paid" for four different interest rates (5%, 10%, 15%, and 18%). The bank's profit from the loan is the total amount paid by the borrower minus the original principal of \$10,000. Higher interest rates are associated with both higher potential profits (as more interest is collected) and increased risk of default.

  1. Calculating Bank Profit

We calculate the interest earned (the bank's profit) for each given rate by subtracting the \$10,000 principal from the "Total paid" value provided in the table:

  • For 5%: \(\$11,322.00 - \$10,000.00 = \$1,322.00\)
  • For 10%: \(\$12,750.00 - \$10,000.00 = \$2,750.00\)
  • For 15%: \(\$14,274.00 - \$10,000.00 = \$4,274.00\)
  • For 18%: \(\$15,234.00 - \$10,000.00 = \$5,234.00\)

Comparing these amounts, the bank earns the most money at the 18% interest rate, collecting \$5,234 in interest.

  1. Conclusion

Since the 18% interest rate generates the highest interest income for the bank, and higher interest rates are generally linked to a greater risk of loan default, we conclude that 18% is the rate at which the bank makes the most money and takes the most risk. The correct option is 18 percent. The final answer is \(\boxed{18}\) percent.

Examples

Understanding how interest rates affect total loan costs is a fundamental skill in personal finance. For example, if you are planning to take out a student loan or a car loan, comparing different interest rates helps you estimate not only your monthly payments but also the total interest you will pay over the life of the loan. Knowing that higher rates result in significantly larger total payments allows you to make informed decisions about whether to pay off a loan early or shop around for a more favorable rate, ultimately helping you manage your debt more effectively.

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