The price of a new car is $24,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 10%/year compounded monthly. (Round your answers to the nearest cent.)

Question

The price of a new car is $24,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 10%/year compounded monthly. (Round your answers to the nearest cent.)

(a) What monthly payment will she be required to make if the car is financed over a period of 36 months? Over a period of 48 months?

(b) What will the interest charges be if she elects the 36-month plan? The 48-month plan?

I do not know where to start, or what to do with the 25% in the formula?

Answer 1

The 25% means that she pays up front $6000 so she only needs to finance $18000.

Over a period of 36 months,
n=36=periods of one month
i, monthly interest = 0.1/12
P, principal = 18000
R=rate=1+i=1+1/120
Monthly payment, A
=PRⁿ(R-1)/(Rⁿ-1)
=18000*(1+1/120)³⁶*(1/120)/((1+1/120)³⁶-1)
=$580.81

Similarly, for 48-month loan,
Monthly payment, A
=PRⁿ(R-1)/(Rⁿ-1)
=18000*(1+1/120)⁴⁸*(1/120)/((1+1/120)⁴⁸-1)
=$456.53

For interest charges, subtract $18000 from the product of monthly payment multiplied by the number of payments.

Answer 2

Well, let me break it down for you, but in a slightly clown-y way!

To start, let's figure out the amount of the down payment. Since it's 25% of $24,000, we can calculate it by doing some clown-y math: 25% of $24,000 is like having one-fourth of 24 elephants, which gives us $6,000.

Now, let's find out how much she needs to finance. Subtract the down payment from the total cost of the car. So, $24,000 - $6,000 = $18,000.

To calculate the monthly payments, we need to use some formulas that involve the loan amount, interest rate, and loan term. Since it's compounded monthly at a rate of 10% per year, we divide the annual rate by 12 months to get the monthly interest rate. It's like dividing a pizza into 12 slices, with one slice representing a month.

Now let's calculate the monthly payments for both the 36-month and 48-month plans.

For the 36-month plan, we'll use the clown calculator, which enjoys dividing cheese (interest) on pizzas (loans). Using the formula for monthly payment calculation, the clown tells me that the monthly payment for a $18,000 loan over 36 months at a 10% interest rate compounded monthly is approximately $594.57.

For the 48-month plan, we'll use the same clown calculator, but it will have a slightly different pizza slicing method. The monthly payment for a $18,000 loan over 48 months at a 10% interest rate compounded monthly is around $468.62.

Now, let's move on to interest charges.

For the 36-month plan, the interest charges will just be the total of all the monthly payments minus the loan amount. So, it's like paying for all those pizzas but keeping in mind how much the loan was. The interest charges for this plan amount to roughly $2,603.92.

For the 48-month plan, the interest charges are slightly different. Again, it's like paying for all those pizzas, but over a longer time. The interest charges for this plan are approximately $3,569.76.

I hope this clown-y explanation helped! Just remember to take these numbers with a pinch of clown humor.

Answer 3

To answer these questions, we will first calculate the loan amount based on the down payment and the price of the car, and then use the loan amount to calculate the monthly payments and interest charges.

(a) To calculate the loan amount, we need to subtract the down payment from the price of the car. The down payment is 25% of $24,000, which is $(24,000 * 0.25) = $6,000.

So, the loan amount is $24,000 - $6,000 = $18,000.

To calculate the monthly payment, we will use the formula for the monthly payment on a loan:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

where M is the monthly payment, P is the principal loan amount, r is the monthly interest rate, and n is the number of monthly payments.

For 36 months:
The interest rate is 10% per year compounded monthly, so the monthly interest rate is 10% / 12 = 0.10 / 12 = 0.00833.

Plugging in the values into the formula:
M = 18,000 * (0.00833 * (1 + 0.00833)^36) / ((1 + 0.00833)^36 - 1)

Using a calculator, the monthly payment for the 36-month plan is approximately $544.15.

For 48 months:
Using the same formula, with n = 48:
M = 18,000 * (0.00833 * (1 + 0.00833)^48) / ((1 + 0.00833)^48 - 1)

Using a calculator, the monthly payment for the 48-month plan is approximately $421.04.

(b) To calculate the interest charges, we need to subtract the loan amount from the total amount paid over the loan term.

For the 36-month plan:
The total amount paid is the monthly payment multiplied by the number of payments:
Total amount paid = Monthly payment * Number of payments = $544.15 * 36 = $19,587.40

The interest charges are the total amount paid minus the loan amount:
Interest charges = Total amount paid - Loan amount = $19,587.40 - $18,000 = $1,587.40

For the 48-month plan:
Using the same method, the total amount paid is $421.04 * 48 = $20,170.92.

The interest charges for the 48-month plan are $20,170.92 - $18,000 = $2,170.92.

So, the interest charges for the 36-month plan are approximately $1,587.40, and for the 48-month plan are approximately $2,170.92.

Answer 4

To calculate the monthly payment and interest charges for financing a car, you can follow these steps:

Step 1: Calculate the loan amount
Given that the price of the car is $24,000 and the down payment is 25% of the purchase price, you can calculate the loan amount by subtracting the down payment from the purchase price:
Loan amount = Purchase price - Down payment
Loan amount = $24,000 - (0.25 * $24,000)
Loan amount = $24,000 - $6,000
Loan amount = $18,000

Step 2: Convert the interest rate to a monthly rate
The interest rate is given as an annual rate of 10%. To calculate the monthly interest rate, divide it by 12:
Monthly interest rate = Annual interest rate / 12
Monthly interest rate = 10% / 12
Monthly interest rate = 0.10 / 12
Monthly interest rate = 0.0083333 (approximately)

Now that you have the loan amount and the monthly interest rate, you can proceed to calculate the monthly payment and interest charges for different financing periods.

(a) Monthly Payments:

For a 36-month period:
To find the monthly payment, you can use the formula for the monthly payment of a loan based on the loan amount, interest rate, and loan term:
Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Number of months))

Substituting the given values:
Monthly payment = ($18,000 * 0.0083333) / (1 - (1 + 0.0083333)^(-36))
Monthly payment ≈ $563.16

For a 48-month period:
Using the same formula, but with 48 months instead of 36:
Monthly payment = ($18,000 * 0.0083333) / (1 - (1 + 0.0083333)^(-48))
Monthly payment ≈ $440.22

(b) Interest Charges:

To find the total interest charges for each financing option, you can multiply the monthly payment by the number of months and then subtract the loan amount:
Interest charges = (Monthly payment * Number of months) - Loan amount

For the 36-month plan:
Interest charges = ($563.16 * 36) - $18,000
Interest charges ≈ $4037.76

For the 48-month plan:
Interest charges = ($440.22 * 48) - $18,000
Interest charges ≈ $4365.06

So, the monthly payments for the 36-month and 48-month plans are approximately $563.16 and $440.22, respectively. The interest charges for these plans are approximately $4037.76 and $4365.06, respectively.