You want to buy a new sports coupe for $85,500, and the finance office at the dealership has quoted you an APR of 6.7 percent for a 72 month loan to buy the car.

You want to buy a new sports coupe for $85,500, and the finance office at the dealership has quoted you an APR of 6.7 percent for a 72 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.)

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)

$85,500 = $C[1 − {1/[1 + (.067/12)]72}/(.067/12)]

Solving for the payment, we get:

C = $85,500/59.15299

C = $1,445.40

To find the EAR, we use the EAR equation:

EAR = [1 + (APR/m)]m − 1

EAR = [1 + (.067/12)]12 − 1

EAR = .0691, or 6.91%

  

Calculator Solution:

  

Enter

72

6.70%/12

±$85,500

N

I/Y

PV

PMT

FV

Solve for

$1,445.40

  

Enter	6.7%						12
		NOM			EFF			C/Y
Solve for				6.91%

Thanks