Question

You want to buy a new sports coupe for $74,500, and the finance office at the dealership has quoted you a loan with an APR of 6.9 percent for 36 months to buy the car.

Required:
a. What will your monthly payments be?
b. What is the effective annual rate on this loan?

Answer 1

The monthly payment for a $74,500 loan with an APR of 6.9% for 36 months is approximately $2,279.58. The effective annual rate on this loan is around 7.06%.

Step-by-step explanation:

To calculate the monthly payments on a loan, you can use the formula:

Monthly Payment = Principal * (r * (1+r)^n) / ((1+r)^n - 1)

Where:

Principal is the loan amount, which in this case is $74,500.

r is the monthly interest rate, which can be calculated by dividing the APR by 12 and converting it to a decimal. In this case, it would be 6.9% / 12 = 0.00575.

n is the number of months, which is 36.

Plugging in the values, we get:

Monthly Payment = $74,500 * (0.00575 * (1+0.00575)^36) / ((1+0.00575)^36 - 1)

Using a calculator, the monthly payment comes out to be approximately $2,279.58. Therefore, your monthly payment will be around $2,279.58.

To calculate the effective annual rate (EAR), you can use the formula:

EAR = (1 + r/n)^n - 1

Where:

r is the monthly interest rate, which in this case is 6.9% / 12 = 0.00575.

n is the number of compounding periods per year, which is 12 (since it's monthly).

Using the formula, we get:

EAR = (1 + 0.00575/12)^12 - 1

Calculating the value, the EAR comes out to be approximately 0.0706 or 7.06%. Therefore, the effective annual rate on this loan is around 7.06%.

Answer 2

a) Monthly payments = $22,969.38

b) Effective rate of return= 7.12%

Step-by-step explanation:

Loan Amortization: A loan repayment method structured such that a series of equal periodic installments will be paid for certain number of periods to offset both the loan principal amount and the accrued interest.

The monthly installment is computed as follows:

Monthly installment= Loan amount/annuity factor

Loan amount; = 74,500

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

r -monthly rate of interest, n- number of months

r- 6.9%/12 = 0.575 % = 0.00575, n = 36 =

Annuity factor = ( 1- (1+00575)^(-36)/0.00575= 32.434

Monthly installment = Loan amount /annuity factor

= 74,500/32.434= 22,969.38

Required monthly payments = $22,969.38

Effective annual interest rate

Effective rate of return = ((1+r)^n- 1) × 100

where r - monthly interest rate- 6.9%/12 = 0.575%

n- number of months= 12 months

Effective rate of return - (1+00575)^(12) - 1× 100= 7.12%

Effective rate of return= 7.12%