Question

pf.9 loans - homework
score: 4.66/54 answered: 4/18
question 5
you want to buy a $22,000.00 car. you can make a 10% down payment, and will finance the balance with a 5% interest rate for 48 months (4 years). what will your monthly payment be?
my monthly payment will be
hint #1 and hint #2
question help: video 1 video 2

Explanation:

Step1: Calculate down payment and loan amount

Down payment = 10% of $22,000 = $22,000 * 0.1 = $2,200.
Loan amount (P) = $22,000 - $2,200 = $19,800.

Step2: Convert annual rate to monthly rate

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

Step3: Calculate number of payments

Number of months (n) = 48.

Step4: Use loan payment formula

The formula for monthly loan payment is:
$$M = P \times \frac{i(1 + i)^n}{(1 + i)^n - 1}$$
Substitute P = 19800, i = 0.05/12, n = 48:
First, calculate (1 + i)^n:
$$(1 + \frac{0.05}{12})^{48} \approx 1.220895$$
Then, calculate numerator:
$$\frac{0.05}{12} \times 1.220895 \approx 0.005087$$
Denominator:
$$1.220895 - 1 = 0.220895$$
Finally, M = 19800 (0.005087 / 0.220895) ≈ 19800 0.02303 ≈ 456.00 (rounded to two decimal places).

Answer:

\$456.00 (or more precisely, approximately \$455.98 if calculated with more precision, but \$456.00 is a reasonable rounded answer)