Question

You want to buy a $18,000 car. The company is offering a 5% interest rate for 36 months (3 years). What will your monthly payments be?

Answer 1

To calculate the monthly payments for a car loan, you can use the formula for a fixed-rate installment loan:

�

=

�

⋅

�

�

1

−

(

1

+

�

)

−

�

P=

1−(1+r)

−n

r⋅PV

​

Where:

�

P is the monthly payment

�

r is the monthly interest rate (annual interest rate divided by 12)

�

�

PV is the present value, which is the loan amount (in this case, the cost of the car)

�

n is the number of payments (loan term in months)

Given the information you provided:

Annual interest rate: 5%

Loan term: 36 months

Present value (cost of the car): $18,000

Let's plug these values into the formula:

�

=

0.05

12

r=

12

0.05

​

(monthly interest rate)

�

=

36

n=36 (number of payments)

PV = $18,000

Now, calculating the monthly payment:

�

=

(

0.05

12

)

⋅

18000

1

−

(

1

+

0.05

12

)

−

36

P=

1−(1+

12

0.05

​

)

−36

(

12

0.05

​

)⋅18000

​

P \approx $537.84

So, your monthly car payment would be approximately $537.84.

Answer 2

To calculate the monthly payments on a $18,000 car loan with a 5% interest rate for 36 months, you can use the formula for calculating loan payments:

Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Number of months))

First, convert the annual interest rate to a monthly interest rate by dividing it by 12. In this case, the annual interest rate is 5%, so the monthly interest rate would be 5% / 12 = 0.05 / 12 = 0.004167 (approximately).

Next, substitute the values into the formula:

Loan amount = $18,000

Monthly interest rate = 0.004167

Number of months = 36

Plugging these values into the formula, we get:

Monthly payment = (18000 * 0.004167) / (1 - (1 + 0.004167)^(-36))

Simplifying the equation, we have:

Monthly payment = (74.505) / (1 - (1 + 0.004167)^(-36))

Calculating further:

Monthly payment = (74.505) / (1 - (1.004167)^(-36))

Monthly payment = (74.505) / (1 - 0.829001)

Monthly payment = (74.505) / (0.170999)

Monthly payment ≈ $435.10

Therefore, your monthly payments for the $18,000 car loan with a 5% interest rate for 36 months would be approximately $435.10.

Explanation:

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