Questions: Teresa plans to buy a used car that costs 23,000. The dealer requires a 10% down payment. The rest of the cost is financed with a 4-year, fixed-rate amortized auto loan at 9% annual interest with monthly payments. Complete the parts below. Do not round any intermediate computations. Round your final answers to the nearest cent if necessary. If necessary, refer to the list of financial formulas. (a) Find the required down payment. (b) Find the amount of the auto loan. (c) Find the monthly payment.

Teresa plans to buy a used car that costs 23,000. The dealer requires a 10% down payment. The rest of the cost is financed with a 4-year, fixed-rate amortized auto loan at 9% annual interest with monthly payments. Complete the parts below. Do not round any intermediate computations. Round your final answers to the nearest cent if necessary. If necessary, refer to the list of financial formulas. (a) Find the required down payment. (b) Find the amount of the auto loan. (c) Find the monthly payment.
Transcript text: Teresa plans to buy a used car that costs $\$ 23,000$. The dealer requires a $10 \%$ down payment. The rest of the cost is financed with a 4 -year, fixed-rate amortized auto loan at $9 \%$ annual interest with monthly payments. Complete the parts below. Do not round any intermediate computations. Round your final answers to the nearest cent if necessary. If necessary, refer to the list of financial formulas. (a) Find the required down payment. $\square$ (b) Find the amount of the auto loan. $\$ \square$ (c) Find the monthly payment. \$ $\square$
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Solution

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Solution Steps

Step 1: Calculate the Required Down Payment

To calculate the required down payment, multiply the cost of the vehicle by the down payment percentage:

\[ \text{Down Payment} = 23000 \times \frac{10}{100} = 2300 \]

Step 2: Determine the Amount of the Auto Loan

The auto loan amount is the cost of the vehicle minus the down payment:

\[ \text{Auto Loan Amount} = 23000 - 2300 = 20700 \]

Step 3: Calculate the Monthly Payment

Using the formula for a fixed-rate amortized loan, where \(P\) is the principal amount, \(r\) is the annual interest rate in decimal form, and \(n\) is the total number of payments:

\[ \text{Monthly Payment} = \frac{20700 \times \frac{9}{1200}}{1 - (1 + \frac{9}{1200})^{-48}} = 515.12 \]

Final Answer:

The required down payment is $2300, the auto loan amount is $20700, and the monthly payment for the auto loan is $515.12.

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