Question

You want to buy a new sports coupe for $91,500, and the finance office at the dealership has quoted you an APR of 7.3 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.)

Answer 1

Answer:

Monthly payment: 1,573.20

effective rate: 7.55%

Explanation:

We need to calculate the quota of an ordinary annuity

The formula for this is as follow:

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV  $91,500.00

time 72 months

rate 0.006083333 the APR is divide into 12 to convert to monthly rate

$91500 \div \frac{1-(1+0.0060833)^{-72} }{0.0060833} = C$

C  $ 1,573.199

The effective rate will be an annual rate equivalent to the APR compounding monthly

$(1+ r)^{time} = 1+ r_e$

time 12.00

rate 0.00608333333333333

$1(1+ 0.00608333333333333)^{12} = 1 + r_e$

1.075493 - 1 = re

re = 0.75493 = 7.55%