Question

ou want to buy a new sports coupe for $81,500, and the finance office at the dealership has quoted you an APR of 6.3 percent for a 60 month loan to buy the car. a. What will your monthly payments be? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What is the effective annual rate on this loan? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

a. The monthly payment will be $1,664.91.

b. The effective annual rate on this loan is 6.49%.

Explanation:

a. What will your monthly payments be? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

This is calculated by using the formula for calculating the present value of an ordinary annuity as follows:

PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV = Present value or price of  new sports coupe = $81,500

P = Monthly payment = ?

r = Monthly interest rate = Annual percentage rate (APR) = 6.3% / 12 = 0.063 / 12 = 0.00525

n = number of months = 60

Substitute the values into equation (1) and solve for P as follows:

85,500 = P * ((1 - (1 / (1 + 0.00525))^60) / 0.00525)

85,500 = P * 51.3541976210894

P = 85,500 / 51.3541976210894

P = $1,664.91

Therefore, the monthly payment will be $1,664.91.

b. What is the effective annual rate on this loan? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Effective annual rate (EAR) refers to the interest rate that is received by an investor in a year after adjusting for compounding.

Since the APR in the question is paid monthly, it implies that it is compounded monthly and the EAR can be computed using the following formula:

EAR = ((1 + (APR / n))^n) - 1 .............................(1)

Where;

APR = 6.3% = 0.063

n = Number of compounding periods or months in a year = 12 months

Substituting the values into equation (1), we have:

EAR = ((1 + (0.063 / 12))^12) - 1

EAR = 1.06485133891298 - 1

EAR = 0.06485133891298

EAR = 6.485133891298%

EAR = 6.49% rounded to 2 decimal places

Therefore, the effective annual rate on this loan is 6.49%.