Questions: Yoko is taking out a mortgage for 264,000 to buy a new house 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 mortgage 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) Her credit union has offered her a 40-year mortgage loan at an annual interest rate of 1.7%. Find the monthly payment. (b) An online lending company has offered her a 40-year mortgage loan at an annual interest rate of 2.1%. Find the monthly payment. (c) Suppose Yoko pays the monthly payment each month for the full term. Which lender's mortgage loan would have the lowest total amount to pay off, and by how much? Credit union The total amount paid would be less than to the online lending company. Online lending company The total amount paid would be less than to the credit union.

Yoko is taking out a mortgage for 264,000 to buy a new house 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 mortgage 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) Her credit union has offered her a 40-year mortgage loan at an annual interest rate of 1.7%. Find the monthly payment. (b) An online lending company has offered her a 40-year mortgage loan at an annual interest rate of 2.1%. Find the monthly payment. (c) Suppose Yoko pays the monthly payment each month for the full term. Which lender's mortgage loan would have the lowest total amount to pay off, and by how much? Credit union The total amount paid would be less than to the online lending company. Online lending company The total amount paid would be less than to the credit union.
Transcript text: Yoko is taking out a mortgage for $\$ 264,000$ to buy a new house 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 mortgage 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) Her credit union has offered her a 40-year mortgage loan at an annual interest rate of $1.7 \%$. Find the monthly payment. $\$$ $\square$ (b) An online lending company has offered her a 40 -year mortgage loan at an annual interest rate of $2.1 \%$. Find the monthly payment. s $\square$ (c) Suppose Yoko pays the monthly payment each month for the full term. Which lender's mortgage loan would have the lowest total amount to pay off, and by how much? Credit union The total amount paid would be $s \square$ less than to the online lending company. Online lending company The total amount paid would be $\$ \square$ $\square$ less than to the credit union.
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Solution

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Solution Steps

Step 1: Calculate Monthly Payment for Credit Union

Using the formula for monthly mortgage payments, we find the monthly payment for the credit union's offer with an annual interest rate of \(1.7\%\): \[ M_{\text{credit union}} = 758.41 \]

Step 2: Calculate Monthly Payment for Online Lending Company

Next, we calculate the monthly payment for the online lending company's offer with an annual interest rate of \(2.1\%\): \[ M_{\text{online}} = 813.42 \]

Step 3: Calculate Total Amount Paid Over the Life of the Loan

Now, we compute the total amount paid over the life of the loan for both offers:

  • For the credit union: \[ \text{Total Paid}_{\text{credit union}} = 364035.18 \]
  • For the online lending company: \[ \text{Total Paid}_{\text{online}} = 390441.49 \]
Step 4: Compare Total Amounts to Determine the Better Deal

Comparing the total amounts paid: \[ \text{Total Paid}_{\text{credit union}} < \text{Total Paid}_{\text{online}} \] Thus, the credit union's mortgage loan is the better deal. The difference in total amounts is: \[ \text{Amount Saved} = 390441.49 - 364035.18 = 26306.31 \]

Final Answer

The credit union's mortgage loan is the better deal, and the total amount paid would be \(\$26306.31\) less than that of the online lending company.

\(\boxed{\text{Credit union; Amount saved: } 26306.31}\)

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