Questions: Keisha is taking out an amortized loan for 81,000 to open a small business and is deciding between the offers from two lenders. She wants to know which one would be the better deal over the life of the small business loan, and by how much. Answer each part. Do not round intermediate computations, and round your answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) A savings and loan association has offered her a 10 -year small business loan at an annual interest rate of 11.2%. Find the monthly payment. (b) Her credit union has offered her a 8 -year small business loan at an annual interest rate of 10.9%. Find the monthly payment. (c) Suppose Keisha pays the monthly payment each month for the full term. Which lender's small business loan would have the lowest total amount to pay off, and by how much? Savings and loan association The total amount paid would be less than to the credit union. Credit union The total amount paid would be less than to the savings and loan association.

Keisha is taking out an amortized loan for 81,000 to open a small business and is deciding between the offers from two lenders. She wants to know which one would be the better deal over the life of the small business loan, and by how much. Answer each part. Do not round intermediate computations, and round your answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) A savings and loan association has offered her a 10 -year small business loan at an annual interest rate of 11.2%. Find the monthly payment. (b) Her credit union has offered her a 8 -year small business loan at an annual interest rate of 10.9%. Find the monthly payment. (c) Suppose Keisha pays the monthly payment each month for the full term. Which lender's small business loan would have the lowest total amount to pay off, and by how much? Savings and loan association The total amount paid would be less than to the credit union. Credit union The total amount paid would be less than to the savings and loan association.
Transcript text: Keisha is taking out an amortized loan for $\$ 81,000$ to open a small business and is deciding between the offers from two lenders. She wants to know which one would be the better deal over the life of the small business loan, and by how much. Answer each part. Do not round intermediate computations, and round your answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) A savings and loan association has offered her a 10 -year small business loan at an annual interest rate of $11.2 \%$. Find the monthly payment. (b) Her credit union has offered her a 8 -year small business loan at an annual interest rate of $10.9 \%$. Find the monthly payment. (c) Suppose Keisha pays the monthly payment each month for the full term. Which lender's small business loan would have the lowest total amount to pay off, and by how much? Savings and loan association The total amount paid would be $\$ \square$ less than to the credit union. Credit union The total amount paid would be $\square$ less than to the savings and loan association.
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Solution

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Solution Steps

Step 1: Calculate Monthly Payment for Savings and Loan Association

For the savings and loan association, the monthly payment \( M_a \) is calculated as follows:

\[ M_a = 1124.9649 \]

Step 2: Calculate Monthly Payment for Credit Union

For the credit union, the monthly payment \( M_b \) is calculated as follows:

\[ M_b = 1268.0177 \]

Step 3: Calculate Total Amount Paid for Each Loan

The total amount paid over the life of the loans is calculated as follows:

  • Total amount paid to the savings and loan association:

\[ \text{Total Paid}_a = 134995.7859 \]

  • Total amount paid to the credit union:

\[ \text{Total Paid}_b = 121729.7035 \]

Step 4: Determine the Cheaper Loan

Comparing the total amounts paid:

\[ \text{Total Paid}_a > \text{Total Paid}_b \]

Thus, the credit union offers the better deal. The difference in total amounts paid is:

\[ \text{Difference} = 134995.7859 - 121729.7035 = 13166.0824 \]

Final Answer

The monthly payment for the savings and loan association is \( M_a = 1124.96 \), the monthly payment for the credit union is \( M_b = 1268.02 \), and the credit union is the better deal by \( \boxed{13166.08} \).

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