Follow The Steps Above To Find { C $}$, The Total Of The Payments, And The Monthly Payment. Choose The Right Answers.Jane Smart Buys A New SUV. The Price, Including Tax, Is { $ 22,500.00$}$. She Finances The Vehicle Over 60 Months
Calculating the Total Payments and Monthly Payment for Jane Smart's SUV
Understanding the Problem
Jane Smart has purchased a new SUV with a price, including tax, of $22,500.00. She has decided to finance the vehicle over a period of 60 months. To determine the total payments and monthly payment, we need to follow a series of steps.
Step 1: Determine the Monthly Payment
To calculate the monthly payment, we need to use the formula for calculating monthly payments on a loan:
M = P[r(1+r)n]/[(1+r)n – 1]
Where:
- M = monthly payment
- P = principal loan amount (the initial amount borrowed)
- r = monthly interest rate (the interest rate divided by 12)
- n = number of payments (the number of months the loan is for)
Step 2: Determine the Interest Rate
Since we do not have the interest rate, we will assume a fixed interest rate of 5% per annum. This is a common interest rate for car loans.
Step 3: Calculate the Monthly Interest Rate
To calculate the monthly interest rate, we divide the annual interest rate by 12:
r = 5%/12 = 0.004167
Step 4: Calculate the Monthly Payment
Now we can plug in the values into the formula:
M = 22500[0.004167(1+0.004167)60]/[(1+0.004167)60 – 1]
M ≈ 425.19
Step 5: Calculate the Total Payments
To calculate the total payments, we multiply the monthly payment by the number of payments:
Total Payments = M x n = 425.19 x 60 ≈ 25511.40
Step 6: Calculate the Total Amount Paid
The total amount paid is the sum of the principal loan amount and the total payments:
Total Amount Paid = P + Total Payments = 22500 + 25511.40 ≈ 48011.40
Conclusion
Based on the calculations above, Jane Smart's monthly payment for her SUV would be approximately $425.19. The total payments over the 60-month period would be approximately $25,511.40. The total amount paid, including the principal loan amount and interest, would be approximately $48,011.40.
Calculating the Total Payments and Monthly Payment for Jane Smart's SUV
| Month | Monthly Payment | Total Payments |
|---|---|---|
| 1 | 425.19 | 425.19 |
| 2 | 425.19 | 850.38 |
| 3 | 425.19 | 1275.57 |
| 4 | 425.19 | 1700.76 |
| 5 | 425.19 | 2125.95 |
| 6 | 425.19 | 2551.14 |
| 7 | 425.19 | 2976.33 |
| 8 | 425.19 | 3401.52 |
| 9 | 425.19 | 3826.71 |
| 10 | 425.19 | 4251.90 |
| 11 | 425.19 | 4677.09 |
| 12 | 425.19 | 5102.28 |
| 13 | 425.19 | 5527.47 |
| 14 | 425.19 | 5952.66 |
| 15 | 425.19 | 6377.85 |
| 16 | 425.19 | 6802.04 |
| 17 | 425.19 | 7226.23 |
| 18 | 425.19 | 7650.42 |
| 19 | 425.19 | 8074.61 |
| 20 | 425.19 | 8498.80 |
| 21 | 425.19 | 8922.99 |
| 22 | 425.19 | 9347.18 |
| 23 | 425.19 | 9771.37 |
| 24 | 425.19 | 10195.56 |
| 25 | 425.19 | 10619.75 |
| 26 | 425.19 | 11043.94 |
| 27 | 425.19 | 11468.13 |
| 28 | 425.19 | 11892.32 |
| 29 | 425.19 | 12316.51 |
| 30 | 425.19 | 12740.70 |
| 31 | 425.19 | 13164.89 |
| 32 | 425.19 | 13589.08 |
| 33 | 425.19 | 14013.27 |
| 34 | 425.19 | 14437.46 |
| 35 | 425.19 | 14861.65 |
| 36 | 425.19 | 15285.84 |
| 37 | 425.19 | 15709.03 |
| 38 | 425.19 | 16132.22 |
| 39 | 425.19 | 16555.41 |
| 40 | 425.19 | 16978.60 |
| 41 | 425.19 | 17401.79 |
| 42 | 425.19 | 17824.98 |
| 43 | 425.19 | 18248.17 |
| 44 | 425.19 | 18671.36 |
| 45 | 425.19 | 19094.55 |
| 46 | 425.19 | 19517.74 |
| 47 | 425.19 | 19940.93 |
| 48 | 425.19 | 20364.12 |
| 49 | 425.19 | 20787.31 |
| 50 | 425.19 | 21210.50 |
| 51 | 425.19 | 21633.69 |
| 52 | 425.19 | 22056.88 |
| 53 | 425.19 | 22480.07 |
| 54 | 425.19 | 22903.26 |
| 55 | 425.19 | 23326.45 |
| 56 | 425.19 | 23749.64 |
| 57 | 425.19 | 24172.83 |
| 58 | 425.19 | 24595.02 |
| 59 | 425.19 | 25017.21 |
| 60 | 425.19 | 25439.40 |
Total Payments: $25,511.40
Total Amount Paid: $48,011.40
Monthly Payment: $425.19
Calculating the Total Payments and Monthly Payment for Jane Smart's SUV: Q&A
Q: What is the formula for calculating the monthly payment on a loan?
A: The formula for calculating the monthly payment on a loan is:
M = P[r(1+r)n]/[(1+r)n – 1]
Where:
- M = monthly payment
- P = principal loan amount (the initial amount borrowed)
- r = monthly interest rate (the interest rate divided by 12)
- n = number of payments (the number of months the loan is for)
Q: How do I calculate the monthly interest rate?
A: To calculate the monthly interest rate, you divide the annual interest rate by 12. For example, if the annual interest rate is 5%, the monthly interest rate would be:
r = 5%/12 = 0.004167
Q: What is the total payments and how is it calculated?
A: The total payments is the sum of the monthly payments over the life of the loan. To calculate the total payments, you multiply the monthly payment by the number of payments:
Total Payments = M x n
Q: What is the total amount paid and how is it calculated?
A: The total amount paid is the sum of the principal loan amount and the total payments:
Total Amount Paid = P + Total Payments
Q: How do I calculate the monthly payment if I don't know the interest rate?
A: If you don't know the interest rate, you can use an online loan calculator or consult with a financial advisor to determine the monthly payment.
Q: Can I use a different formula to calculate the monthly payment?
A: Yes, there are other formulas that can be used to calculate the monthly payment, such as the formula for calculating the monthly payment on a fixed-rate loan:
M = P[r(1+r)n]/[(1+r)n – 1]
However, this formula assumes a fixed interest rate and a fixed number of payments.
Q: How do I calculate the total payments and monthly payment if the loan has a variable interest rate?
A: If the loan has a variable interest rate, you will need to use a more complex formula that takes into account the changing interest rate over time. You can use an online loan calculator or consult with a financial advisor to determine the monthly payment.
Q: Can I use a loan calculator to calculate the total payments and monthly payment?
A: Yes, there are many online loan calculators available that can help you calculate the total payments and monthly payment. These calculators can take into account the principal loan amount, interest rate, and number of payments to give you an estimate of the total payments and monthly payment.
Q: How do I determine the principal loan amount?
A: The principal loan amount is the initial amount borrowed. This is the amount that you will need to repay over the life of the loan.
Q: Can I use a different type of loan to finance my SUV?
A: Yes, there are many different types of loans that you can use to finance your SUV, such as a personal loan, a car loan, or a lease. Each type of loan has its own advantages and disadvantages, and you should carefully consider your options before making a decision.
Q: How do I choose the right loan for my SUV?
A: To choose the right loan for your SUV, you should consider the following factors:
- The interest rate: Look for a loan with a low interest rate to save money on interest.
- The term: Consider a loan with a longer term to reduce your monthly payments.
- The fees: Look for a loan with low fees to save money.
- The repayment terms: Consider a loan with flexible repayment terms to fit your budget.
By considering these factors, you can choose the right loan for your SUV and ensure that you are getting the best deal possible.