Interest and Total Payments on 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[tex]$ \\
\hline
\end{tabular}

1. The bank would earn a profit of $[/tex]\square[tex]$ over $[/tex]\square[tex]$ years if a customer was charged $[/tex]15 \%[tex]$ interest.

2. A consumer would save $[/tex]\square[tex]$ over the life of the loan with a $[/tex]5 \%[tex]$ interest rate rather than a $[/tex]10 \%$ interest rate.



Answer :

To determine the solutions, we need to follow these steps:

1. Calculate the profit that the bank would earn if a customer was charged a 15% interest rate over a period of 5 years:

- The loan amount is \[tex]$10,000. - At a 15% interest rate, the total amount paid over the 5 years is \$[/tex]14,274.
- The profit for the bank is the total amount paid minus the initial loan amount.
- Profit = \[tex]$14,274 - \$[/tex]10,000 = \[tex]$4,274. 2. Calculate the savings for a consumer over the life of the loan with a 5% interest rate instead of a 10% interest rate: - At a 5% interest rate, the total amount paid over 5 years is \$[/tex]11,322.
- At a 10% interest rate, the total amount paid over 5 years is \[tex]$12,750. - The savings for the consumer would be the difference between the total amounts paid at the two different interest rates. - Savings = \$[/tex]12,750 - \[tex]$11,322 = \$[/tex]1,428.

Using these calculations, we can fill in the blanks:

- The bank would earn a profit of \[tex]$4,274 over 5 years if a customer was charged 15% interest. - A consumer would save \$[/tex]1,428 over the life of the loan with a 5% interest rate rather than a 10% interest rate.

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