Question

You want to buy a new sports coupe for $84,500, and the finance office at the dealership has quoted you an APR of 5.2 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 1

Answer:

Monthly Payment is $1602.37

Effective interest rate is 5.33%

Explanation:

a.

The monthly payment made includes the interest and principal payment as well.

Monthly payment can be calculated using following formula

Monthly Payment = [Present value of loan x r] / [{1 - (1 + r)-n}]

Monthly Payment = [$84,500 x (0.052/12)] / [1 - (1 + 0.052/12)-60]

Monthly Payment = [$366.17 / 0.2285]

Monthly Payment = $1,602.37

b.

The Effective interest rate is the actual interest rate that are being charged on loan after incorporating the compounding effect.

Use following formula to calculate the effective Annual rate

EAR = [1 + (i/n)]^n - 1

EAR  = [ 1 + (5.2% / 12]^12 - 1

EAR = [1.0043]^12 - 1

EAR = 1.0533 - 1

EAR = 0.0533

EAR = 5.33%