Questions: Assignment - 7. Automobile Loans Attempt 1 of 10 Use the formula to solve for c. Choose the right answer. Amount Financed (m)= 600 Number of Payments per year (y)=12 Number of Payments (n)=24 APR (0) =18 % c=

Solution Steps

To solve for the monthly payment \( c \) of an automobile loan, we can use the formula for calculating the monthly payment on an installment loan:

\[ c = \frac{m \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \]

where:

• \( m \) is the amount financed
• \( r \) is the monthly interest rate (APR divided by 12)
• \( n \) is the total number of payments

Given:

• Amount Financed \( m = \$600 \)
• Number of Payments per year \( y = 12 \)
• Number of Payments \( n = 24 \)
• APR \( = 18\% \)

First, convert the annual percentage rate (APR) to a monthly interest rate by dividing by 12. Then, use the formula to calculate the monthly payment \( c \).

We are given the following values for the automobile loan:

• Amount Financed \( m = 600 \)
• Number of Payments per year \( y = 12 \)
• Total Number of Payments \( n = 24 \)
• Annual Percentage Rate \( \text{APR} = 18\% \)

To find the monthly interest rate \( r \), we convert the APR from a percentage to a decimal and divide by the number of payments per year: \[ r = \frac{18}{100} \div 12 = 0.015 \]

Using the formula for the monthly payment \( c \): \[ c = \frac{m \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \] Substituting the known values: \[ c = \frac{600 \cdot 0.015 \cdot (1 + 0.015)^{24}}{(1 + 0.015)^{24} - 1} \] Calculating this gives: \[ c \approx 29.9545 \] Rounding to four significant digits, we have: \[ c \approx 29.95 \]

Final Answer