You wish to purchase a new car and can afford monthly repayments of up to $250 per month. You see a car you like for $12,000 and

Question

Nutka1998 [239]

3 years ago

15

You wish to purchase a new car and can afford monthly repayments of up to $250 per month. You see a car you like for $12,000 and

are offered financing to secure the purchase. The loan lasts for 5 years and the annual interest rate is 17.9%. Can you afford to purchase the car on finance?

Mathematics

1 answer:

White raven [17] · Answer 1 · 2022-05-24T19:10:27+03:00

Answer:

Since the finance’s monthly required payment of $304.07 is greater than the $250 monthly that you can afford, this implies that you CANNOT afford to purchase the car on finance.

Step-by-step explanation:

The monthly required payment of the finance can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PV = M * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV = Present value or finance amount = $12,000

M = Finance’s monthly required payment = ?

r = Monthly interest rate = Annual interest rate / 12 = 17.9% / 12 = 0.179 / 12 = 0.0149166666666667

n = number of months = Number of years * 12 = 5 * 12 = 60

Substitute the values into equation (1) and solve for M, we have:

$12,000 = M * ((1 - (1 / (1 + 0.0149166666666667))^60) / 0.0149166666666667)

$12,000 = M * 39.464764662266

M = $12,000 / 39.464764662266 = $304.07

Since the finance’s monthly required payment of $304.07 is greater than the $250 monthly that you can afford, this implies that you CANNOT afford to purchase the car on finance.