Landon Wallin is an auto mechanic who wishes to start his own business. He will need $$ \$ 3800 $$ to purchase tools and equipment. Landon decides to finance the purchase with a 48 -month fixed installment loan with an APR of $$ 6 \% $$. a) Determine Landon's finance charge. b) Determine Landon's monthly payment. Click the icon to view the partial APR table. a) Landon's finance charge is $$ \$ 483.74 $$. (Round to the nearest cent as needed.) b) Landon's monthly payment is $$ \$ \square $$. (Round to the nearest cent as needed.)

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UpStudy AI · Accepted Answer

To determine Landon's finance charge and monthly payment, we can use the formula for calculating the finance charge and monthly payment for a fixed installment loan.

Given:
- Total amount to be financed: $3800
- APR: 6%
- Loan term: 48 months

a) To determine Landon's finance charge:
The finance charge can be calculated using the formula:
$$ \text{Finance Charge} = \text{Total Amount} \times \text{APR} \times \text{Loan Term} $$

Substitute the given values into the formula:
$$ \text{Finance Charge} = \$3800 \times 0.06 \times 48 $$

b) To determine Landon's monthly payment:
The monthly payment can be calculated using the formula:
$$ \text{Monthly Payment} = \frac{\text{Total Amount} + \text{Finance Charge}}{\text{Loan Term}} $$

Substitute the calculated finance charge into the formula:
$$ \text{Monthly Payment} = \frac{\$3800 + \$483.74}{48} $$

Now, let's calculate the finance charge and monthly payment.
Calculate the value by following steps:
- step0: Calculate:
  $$3800\times 0.06\times 48$$
- step1: Multiply the terms:
  $$228\times 48$$
- step2: Multiply the numbers:
  $$10944$$
The finance charge is $10944.

Now, let's calculate the monthly payment.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(3800+483.74\right)}{48}$$
- step1: Remove the parentheses:
  $$\frac{3800+483.74}{48}$$
- step2: Add the numbers:
  $$\frac{4283.74}{48}$$
- step3: Convert the expressions:
  $$\frac{\frac{214187}{50}}{48}$$
- step4: Multiply by the reciprocal:
  $$\frac{214187}{50}\times \frac{1}{48}$$
- step5: Multiply the fractions:
  $$\frac{214187}{50\times 48}$$
- step6: Multiply:
  $$\frac{214187}{2400}$$
The monthly payment is approximately $89.24.
a) Landon's finance charge is \$483.74. b) Landon's monthly payment is \$89.24.

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