Question

You want to buy a new sports coupe for $75,500, and the finance office at the dealership has quoted you a 7.9 percent APR loan for 72 months to buy the car. Requirement 1: What will your monthly payments be? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places

Answer 1

To determine the monthly payment for a $75,500 car loan at a 7.9% APR for 72 months, we convert the APR to a monthly rate and plug it into the installment loan payment formula. After performing the calculation, the estimated monthly payment is approximately $1,342.05.

Step-by-step explanation:

To determine the monthly payments for a car loan of $75,500 with a 7.9% APR for 72 months, we will need to use the formula for an installment loan payment which is given by:

P = [PV x i] / [1 - (1 + i)⁻ⁿ]

Where:

• PV = Present Value (amount of loan, in this case, $75,500)
• i = monthly interest rate (APR divided by 12)
• n = total number of payments (loan term in months, in this case, 72)

Firstly, we convert the APR to a monthly interest rate:

i = 7.9% / 12 = 0.6575% per month

Next, we plug the values into the formula:

P = [75,500 x 0.006575] / [1 - (1 + 0.006575)⁻⁷²]

After calculating using the formula, you would find the monthly payment to be approximately $1,342.05 (calculations should be performed with a calculator or software for accurate results).

Answer 2

$1,295.03

Step-by-step explanation:

To find the answer, we will use the present value of an annuity formula:

PV = A ( 1 - (1 + i)^-n) / i

Where:

• PV = Present Value of the investment (in this case, the value of the loan)
• A = Value of the Annuity (which will be our incognita)
• i = interest rate
• n = number of compounding periods

Now, we convert the 7.9 APR to a monthly rate. The result is a 0.6% monthly rate.

Finally, we plug the amounts into the formula, and solve:

75,500 = A (1 - (1 + 0.006)^-72) / 0.006

75,500 = A (58.3)

75,500 / 58.3 = A

1,295.03 = A

Thus, the monthly payments of the car loan will be $1,295.03 each month.