You want to buy a new sports coupe for $76,500, and the finance office at the de

Question

You want to buy a new sports coupe for $76,500, and the finance office at the dealership has quoted you a 5.8 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))

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))

You want to buy a new sports coupe for $76,500, and the finance office at the dealership has quoted you a 5.8 percent APR loan for 72 months to buy the car.

Explanation / Answer

Answer: 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

$76500=C[1-{1/[1+(0.058/12)]72 /0.058/12

Solving for the payment we get:

C=$76500/60.6846

C=$1261

EAR=[1+(APR/m)]m - 1

=[1+(0.058/12)]12 -1

=5.9566%

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