You want to buy a new sports coupe for $73,500, and the finance office at the dealership has quoted you a 5.5 percent APR loan for 72 months to buy the car.

You want to buy a new sports coupe for $73,500, and the finance office at the dealership has quoted you a 5.5 percent APR loan for 72 months to buy the car.

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

Monthly payment

$

What is the effective annual rate on this loan? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Effective annual rate

%

Explanation:

We first need to find the annuity payment. We have the PVA, the length of the annuity, and the interest rate. Using the PVA equation:

PVA = C({1 − [1 / (1 + r)t]} / r)

$73,500 = $C[1 − {1 / [1 + (0.055/12)]72} / (0.055/12)]

Solving for the payment, we get:

C = $73,500 / 61.20742 = $1,200.83

To find the EAR, we use the EAR equation:

EAR = [1 + (APR / m)]m − 1

EAR = [1 + (0.055 / 12)]12 − 1 = 0.0564, or 5.64%

 

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

 

Enter

72

5.50% / 12

$73,500

N

I/Y

PV

PMT

FV

Solve for

$1,200.83

  

Enter	5.5%						12
		NOM			EFF			C/Y
Solve for				5.64%