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

Monthly payment: 1,573.20

effective rate: 7.55%

Step-by-step explanation:

We need to calculate the quota of an ordinary annuity

The formula for this is as follow:

`PV / (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 / (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%