Question

A cash incentives program to encourage you to purchase a more fuel efficient car rewards you with a ​$5500 credit for trading in an old car provided you purchase a new car with fuel economy at least 10 miles per gallon more than your old car. This​ incentive, along with a​ 0% interest​ loan, was too much to resist. Your car payment is ​$480 per month. Complete parts a through d below. Question content area bottom Part 1 a. Write an equation to determine the total amount p paid on the car after n​ months, including the ​$5500 credit. p equals 480 n plus 5500 Part 2 b. Use the equation you wrote in part a to complete the following table. Number of​ Months, n 1 2 3 4 5 6 Total Amount​ Paid, p​ ($) enter your response here enter your response here enter your response here enter your response here enter your response here enter your response here

Answer 1

To determine the total amount \( p \) paid on the car after \( n \) months, including the $5500 credit, we can use the formula provided:

\[ p = 480n + 5500 \]

Now, let's complete the table for different values of \( n \) (the number of months):

Table of Total Amount Paid

| Number of Months, \( n \) | Total Amount Paid, \( p \) ($) | |---------------------------|-------------------------------| | 1 | \( 480(1) + 5500 = 480 + 5500 = 5980 \) | | 2 | \( 480(2) + 5500 = 960 + 5500 = 6460 \) | | 3 | \( 480(3) + 5500 = 1440 + 5500 = 6940 \) | | 4 | \( 480(4) + 5500 = 1920 + 5500 = 7420 \) | | 5 | \( 480(5) + 5500 = 2400 + 5500 = 7900 \) | | 6 | \( 480(6) + 5500 = 2880 + 5500 = 8380 \) |

Completed Table

| Number of Months, \( n \) | Total Amount Paid, \( p \) ($) | |---------------------------|-------------------------------| | 1 | 5980 | | 2 | 6460 | | 3 | 6940 | | 4 | 7420 | | 5 | 7900 | | 6 | 8380 |

This provides the total amount paid on the car after each specified number of months, incorporating the cash incentive.

Answer 2

After 10 ​months, I paid ​$
  
enter your response here toward the price of the car.

Answer 3

To find the total amount \( p \) paid toward the price of the car after 10 months, we can use the same equation:

\[ p = 480n + 5500 \]

Plugging in \( n = 10 \):

\[ p = 480(10) + 5500 \]

Calculating this:

\[ p = 4800 + 5500 = 10300 \]

Therefore, after 10 months, you paid $10,300 toward the price of the car.

Answer 4

The car you chose cost ​$34 comma 300 including taxes and all fees. How many years will it take you to pay off your​ loan?
It will take
  
enter your response here years to pay off the loan.
​(Simplify your​ answer.)

Answer 5

To determine how many years it will take to pay off the loan for a car that costs $34,300, we first need to calculate the total loan amount, which is the cost of the car minus the cash incentive you received, and then see how long it will take to pay that amount off with the monthly payment of $480.

1. Calculate the loan amount:

\[ \text{Loan Amount} = \text{Cost of Car} - \text{Cash Incentive} \] \[ \text{Loan Amount} = 34300 - 5500 = 28800 \]

2. Calculate the number of months to pay off the loan:

To find the number of months to pay off the loan, we use the formula:

\[ \text{Number of Months} = \frac{\text{Loan Amount}}{\text{Monthly Payment}} \] \[ \text{Number of Months} = \frac{28800}{480} = 60 \]

3. Convert months into years:

Since there are 12 months in a year, we divide the number of months by 12:

\[ \text{Number of Years} = \frac{60}{12} = 5 \]

Conclusion:

It will take 5 years to pay off the loan.

Answer 6

A cash incentives program to encourage you to purchase a more fuel efficient car rewards you with a ​$5500 credit for trading in an old car provided you purchase a new car with fuel economy at least 10 miles per gallon more than your old car. This​ incentive, along with a​ 0% interest​ loan, was too much to resist. Your car payment is ​$390 per month. Complete parts a through d below.
Question content area bottom
Part 1
a. Write an equation to determine the total amount p paid on the car after n​ months, including the ​$5500 credit.
  
p equals 390 n plus 5,500
Part 2
b. Use the equation you wrote in part a to complete the following table.
Number of​ Months, n
1
2
3
4
5
6
Total Amount​ Paid, p​ ($)
  
enter your response here
  
enter your response here
  
enter your response here
  
enter your response here
  
enter your response here
  
enter your response here

Answer 7

To determine the total amount \( p \) paid on the car after \( n \) months, including the $5500 credit, we start with the equation given:

\[ p = 390n + 5500 \]

Now, we can use this equation to calculate the total amount paid for different values of \( n \) (the number of months) and complete the table.

Table of Total Amount Paid

We'll calculate the total amount paid for \( n \) ranging from 1 to 6:

1. For \( n = 1 \): \[ p = 390(1) + 5500 = 390 + 5500 = 5890 \]

2. For \( n = 2 \): \[ p = 390(2) + 5500 = 780 + 5500 = 6280 \]

3. For \( n = 3 \): \[ p = 390(3) + 5500 = 1170 + 5500 = 6670 \]

4. For \( n = 4 \): \[ p = 390(4) + 5500 = 1560 + 5500 = 7060 \]

5. For \( n = 5 \): \[ p = 390(5) + 5500 = 1950 + 5500 = 7450 \]

6. For \( n = 6 \): \[ p = 390(6) + 5500 = 2340 + 5500 = 7840 \]

Completed Table

| Number of Months, \( n \) | Total Amount Paid, \( p \) ($) | |---------------------------|-------------------------------| | 1 | 5890 | | 2 | 6280 | | 3 | 6670 | | 4 | 7060 | | 5 | 7450 | | 6 | 7840 |

Feel free to let me know if you need further assistance!

Answer 8

After 11 ​months, I paid ​$
  
enter your response here toward the price of the car.

Answer 9

To find the total amount \( p \) paid toward the price of the car after 11 months, we can use the equation:

\[ p = 390n + 5500 \]

Substituting \( n = 11 \):

\[ p = 390(11) + 5500 \]

Calculating this:

\[ p = 4290 + 5500 = 9790 \]

Therefore, after 11 months, you paid $9,790 toward the price of the car.

Answer 10

The car you chose cost ​$19 comma 540 including taxes and all fees. How many years will it take you to pay off your​ loan?
It will take
  
enter your response here years to pay off the loan.
​(Simplify your​ answer.)

Answer 11

To determine how many years it will take to pay off the loan for the car that costs $19,540, we first need to calculate the total loan amount, which is the cost of the car minus the cash incentive, and then see how long it will take to pay that amount off with the monthly payment of $390.

1. Calculate the loan amount:

   \[ \text{Loan Amount} = \text{Cost of Car} - \text{Cash Incentive} \] \[ \text{Loan Amount} = 19540 - 5500 = 14040 \]

2. Calculate the number of months to pay off the loan:

   To find the number of months to pay off the loan, use the formula:

   \[ \text{Number of Months} = \frac{\text{Loan Amount}}{\text{Monthly Payment}} \] \[ \text{Number of Months} = \frac{14040}{390} \approx 36 \]

3. Convert months into years:

   Since there are 12 months in a year:

   \[ \text{Number of Years} = \frac{36}{12} = 3 \]

Conclusion:

It will take 3 years to pay off the loan.