Question

pf.9 loans - homework
score: 4.66/54 answered: 3/18
question 4
you want to buy a $19,000.00 car. you can make a 10% down payment, and will finance the balance with a 5% interest rate for 60 months (5 years). what will your monthly payment be?
my monthly payment will be
hint #1 and hint #2

Explanation:

Step1: Calculate down payment and loan amount

Down payment = 10% of $19,000 = $19,000 * 0.1 = $1,900.
Loan amount (P) = $19,000 - $1,900 = $17,100.

Step2: Convert annual interest rate to monthly

Annual interest rate (r) = 5% = 0.05.
Monthly interest rate (i) = 0.05 / 12.

Step3: Number of payments (n)

n = 60 months.

Step4: Use loan payment formula

The formula for monthly payment (M) on a loan is:
$$M = P \times \frac{i(1 + i)^n}{(1 + i)^n - 1}$$
Substitute P = $17,100, i = 0.05/12, n = 60.
First, calculate i = 0.05 / 12 ≈ 0.0041667.
Then, (1 + i)^n = (1 + 0.0041667)^60 ≈ 1.283358679.
Numerator: 0.0041667 * 1.283358679 ≈ 0.0053473.
Denominator: 1.283358679 - 1 = 0.283358679.
M = 17100 (0.0053473 / 0.283358679) ≈ 17100 0.01887 ≈ 322.68.

Answer:

$322.68 (rounded to two decimal places, actual calculation may vary slightly due to rounding during steps)