Questions: Pablo is taking out an amortized loan for 14,000 to buy a new car and is deciding between the offers from two lenders. He wants to know which one would be the better deal over the life of the car 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 him a 7-year car loan at an annual interest rate of 6.3%. Find the monthly payment. (b) An online lending company has offered him a 6-year car-loan at an annual interest rate of 6.1%. Find the monthly payment. (c) Suppose Pablo pays the monthly payment each month for the full term. Which lender's car 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 online lending company. Online lending company The total amount paid would be less than to the savings and loan association.

Pablo is taking out an amortized loan for 14,000 to buy a new car and is deciding between the offers from two lenders. He wants to know which one would be the better deal over the life of the car 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 him a 7-year car loan at an annual interest rate of 6.3%. Find the monthly payment. (b) An online lending company has offered him a 6-year car-loan at an annual interest rate of 6.1%. Find the monthly payment. (c) Suppose Pablo pays the monthly payment each month for the full term. Which lender's car 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 online lending company. Online lending company The total amount paid would be less than to the savings and loan association.
Transcript text: Pablo is taking out an amortized loan for $\$ 14,000$ to buy a new car and is deciding between the offers from two lenders. He wants to know which one would be the better deal over the life of the car 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 him a 7-year car loan at an annual interest rate of $6.3 \%$. Find the monthly payment. $\$ \square$ (b) An online lending company has offered him a 6-year car-loan at an annual interest rate of $6.1 \%$. Find the monthly payment. $\$ \square$ (c) Suppose Pablo pays the monthly payment each month for the full term. Which lender's car 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 online lending company. Online lending company 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 Interest Rates

For Loan 1: $r_{monthly1} = \frac{6.3}{12 \times 100} = 0.00525$ For Loan 2: $r_{monthly2} = \frac{6.1}{12 \times 100} = 0.00508$

Step 2: Calculate Number of Payments

For Loan 1: $N1 = 7 \times 12 = 84$ For Loan 2: $N2 = 6 \times 12 = 72$

Step 3: Calculate Monthly Payments

For Loan 1: $M1 = 14000 \times \frac{0.00525 \times (1 + 0.00525)^{N1}}{(1 + 0.00525)^{N1} - 1} = 206.54$ For Loan 2: $M2 = 14000 \times \frac{0.00508 \times (1 + 0.00508)^{N2}}{(1 + 0.00508)^{N2} - 1} = 232.68$

Step 4: Calculate Total Payments

For Loan 1: $Total1 = M1 \times N1 = 17349.29$ For Loan 2: $Total2 = M2 \times N2 = 16753.09$

Final Answer:

The more cost-effective loan is Loan 2 with a difference of $596.2 over its entire term.

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