You want to buy a new sports coupe for $89,500, and the finance office at the dealership has quoted you an APR of 7.1 percent for a 60 month loan to buy the car. What will your monthly payments be? What is the effective annual rate on this loan?

Answer: a) $1,775.44

b. 7.34%

Explanation:

a) What we are dealing with here is an annuity.

And to find the monthly payments, we can use the Present Value of an annuity formula because we already have the present value of the Annuity.

Formula is,

PV = PMT (1 - (1 + r) ^ - n) / r

Where PV is the present value

PMT is the payment

r is the APR

n is the number of periods.

Because n is in months, APR must be in months too so,

= 7.1%/12

= 0.59%

Calculating therefore would be,

89,500 = PMT (1 - (1 + 0.59%) ^ - 60) / 0.59%

89,500 = PMT (50.41)

PMT = 89,500/50.41

PMT = 1775.44138068

PMT = $1,775.44

The monthly payment is $1,775.44

b) Effective annual rate on this loan = (1+APR/12) ^12 - 1

= (1+7.1%/12) ^12 - 1

= 7.34%

Effective annual rate on this loan is 7.34%

If you need any clarification do comment.