Question

You want to buy a new car. You can afford payments of $ 275 per month and can borrow the money at an interest rate of 4.2 % compounded monthly for 5 years. How much are you able to borro

Answer 1

To determine the maximum loan you can afford, we can use the formula for the present value of an ordinary annuity.

Step-by-step explanation:

To determine the maximum loan you can afford, we can use the formula for the present value of an ordinary annuity:

PV = P * ((1 - (1 + r)-n)) / r

Where:

• PV is the present value of the loan
• P is the monthly payment ($275)
• r is the monthly interest rate (4.2% / 12)
• n is the number of payment periods (5 years * 12)

Plugging in the values, we get:

PV = 275 * ((1 - (1 + 0.042/12)-(5*12))) / (0.042/12)

Solving this equation, PV ≈ $14,210.22. Therefore, you are able to borrow up to $14,210.22 to buy a new car.

Answer 2

You can afford to borrow approximately $13,535.14 with monthly payments of $275 at a 4.2% interest rate compounded monthly over 5 years.

Step-by-step explanation:

To determine how much you are able to borrow with payments of $275 per month at an interest rate of 4.2% compounded monthly for 5 years, we can use the present value of an annuity formula:

PV = PMT * [(1 - (1 + r)^-n) / r]

Where:

• PV = Present Value of the loan (amount you can borrow)
• PMT = Monthly payment ($275)
• r = Monthly interest rate (Annual rate / 12)
• n = Total number of payments (years * 12)

Now we plug in the values:

r = 4.2% / 12 = 0.035%

n = 5 * 12 = 60

So:

PV = $275 * [(1 - (1 + 0.0035)^-60) / 0.0035]

Calculating this, we get:

PV = $275 * [(1 - (1 + 0.0035)^-60) / 0.0035]

PV ≈ $275 * [1 - (1.0035)^-60] / 0.0035

PV ≈ $275 * 49.2186667

PV ≈ $13,535.14

Therefore, you can borrow approximately $13,535.14.

This calculation allows you to understand the maximum loan amount you are able to afford given the monthly payment and interest rate, which is an important aspect of financial planning when considering an auto loan.