Interest and Total Payments for a \[tex]$10,000 Loan over Five Years

\begin{tabular}{|c|c|c|}
\hline \begin{tabular}{c}
Interest \\
rate
\end{tabular} & \begin{tabular}{c}
Monthly \\
payment
\end{tabular} & Total paid \\
\hline $[/tex]5 \%[tex]$ & $[/tex]\[tex]$ 188.70$[/tex] & [tex]$\$[/tex] 11,322.00[tex]$ \\
\hline $[/tex]10 \%[tex]$ & $[/tex]\[tex]$ 212.50$[/tex] & [tex]$\$[/tex] 12,750.00[tex]$ \\
\hline $[/tex]15 \%[tex]$ & $[/tex]\[tex]$ 237.90$[/tex] & [tex]$\$[/tex] 14,274.00[tex]$ \\
\hline $[/tex]18 \%[tex]$ & $[/tex]\[tex]$ 253.90$[/tex] & [tex]$\$[/tex] 15,234.00$ \\
\hline
\end{tabular}

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

A. 5 percent
B. 10 percent
C. 15 percent
D. 18 percent



Answer :

Let's analyze the given data step-by-step to determine at which interest rate the bank makes the most profit.

1. First, we have the initial loan amount, which is [tex]\( \$10,000 \)[/tex], and this amount remains constant regardless of the interest rate.

2. We are given total payments for each interest rate over a five-year period:

- For an interest rate of [tex]\(5\%\)[/tex]:
[tex]\[ \text{Total paid} = \$11,322.00 \][/tex]

- For an interest rate of [tex]\(10\%\)[/tex]:
[tex]\[ \text{Total paid} = \$12,750.00 \][/tex]

- For an interest rate of [tex]\(15\%\)[/tex]:
[tex]\[ \text{Total paid} = \$14,274.00 \][/tex]

- For an interest rate of [tex]\(18\%\)[/tex]:
[tex]\[ \text{Total paid} = \$15,234.00 \][/tex]

3. The profit made by the bank is the total amount paid by the borrower minus the initial loan amount. Let's calculate the profit for each interest rate:

- For [tex]\(5\%\)[/tex]:
[tex]\[ \text{Profit} = \$11,322.00 - \$10,000.00 = \$1,322.00 \][/tex]

- For [tex]\(10\%\)[/tex]:
[tex]\[ \text{Profit} = \$12,750.00 - \$10,000.00 = \$2,750.00 \][/tex]

- For [tex]\(15\%\)[/tex]:
[tex]\[ \text{Profit} = \$14,274.00 - \$10,000.00 = \$4,274.00 \][/tex]

- For [tex]\(18\%\)[/tex]:
[tex]\[ \text{Profit} = \$15,234.00 - \$10,000.00 = \$5,234.00 \][/tex]

4. Now, we compare these profits to determine at which interest rate the bank makes the most money:

- Profit at [tex]\(5\%\)[/tex]: \[tex]$1,322.00 - Profit at \(10\%\): \$[/tex]2,750.00
- Profit at [tex]\(15\%\)[/tex]: \[tex]$4,274.00 - Profit at \(18\%\): \$[/tex]5,234.00

5. Clearly, the profit is highest when the interest rate is [tex]\(18\%\)[/tex].

Therefore, banks make the most money and take the most risk with an interest rate of [tex]\( 18\% \)[/tex].