You want to buy a new sports coupe for $75,300, and the finance office at the dealership has quoted you a loan with an APR of 7.7 percent for 36 months to buy the car. What will your monthly payments be

$2,349.22

Explanation:

Loan amortization is method of loan repayment using a series of equal payments which each installment covering part of the principal and interest.

The monthly payment can be determined as follows:

Monthly payment = Loan amount/Annuity factor

Annuity factor =( 1 - (1+r)^(-n))/r

r - 7.7%/12 = 0.6416% per month

n = 36 months

Annuity factor = (1 - (1.00641)^(-36))/0.00641)

                         =32.0531

Monthly payments =75,300/32.0531

                              = $2,349.22

Monthly payments=  $2,349.22

$2,349.22

Explanation:

Firstly, We need to get the annuity payment. We have the PVA, the length of the annuity, and the interest rate. By applying the PVA equation:

PVA = C({1 – [1/(1 + r)t]} / r)

$75,300 = C[1 – {1 / [1 + (0.077/12)]36} / (0.077/12)]

After Solving for the payment, we have:

C= $75,300 / 32.05318

C= $2,349.22

2:

To be able to solve the EAR, we apply the EAR equation which is :

EAR = [1 + (APR / m)]m– 1

EAR = [1 + (0.077 / 12)]12– 1

EAR = 0.0798 or 7.98%

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