Questions: Find the payment and total amount of interest paid on the installment loan given the following conditions: A 37,000 four-year car loan at an interest rate of 4.4% with quarterly payments. Payment Amount: Total Amount of Interest Paid:

Solution Steps

The annual interest rate is given as \(4.4\%\). To find the quarterly interest rate, we convert it to a decimal and divide by the number of payments per year: \[ \text{Quarterly Interest Rate} = \frac{4.4\%}{4} = 0.011 \]

The loan term is \(4\) years, and since payments are made quarterly, the total number of payments is: \[ \text{Total Payments} = 4 \text{ years} \times 4 \text{ payments/year} = 16 \]

Using the annuity formula, the quarterly payment amount \(P\) can be calculated as follows: \[ P = \frac{37000 \times 0.011}{1 - (1 + 0.011)^{-16}} \approx 2534.6293 \]

The total amount paid over the life of the loan is: \[ \text{Total Amount Paid} = P \times \text{Total Payments} \approx 2534.6293 \times 16 \approx 40554.0683 \]

The total interest paid is the total amount paid minus the principal: \[ \text{Total Interest Paid} = \text{Total Amount Paid} - 37000 \approx 40554.0683 - 37000 \approx 3554.0683 \]

Final Answer