Suppose that you borrow 

​$13 comma 00013,000 

for 

fivefive 

years at 

66​% 

toward the purchase of a car. Use 

PMT equals StartStartFraction Upper P left parenthesis StartFraction r Over n EndFraction right parenthesis OverOver left bracket 1 minus left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript negative nt right bracket EndEndFractionPMT=Prn1−1+rn−nt 

to find the monthly payments and the total interest for the loan.

We will use the loan payment formula to calculate the monthly payments and the total interest for the loan:

### Given information:
- Loan amount $ P $ = $13,000
- Annual interest rate $ r $ = 6% = 0.06
- Loan term $ t $ = 5 years
- $ n $ = 12 (monthly payments)

### Steps:
1. First, calculate the monthly payment using the formula:
   \[
   PMT = \frac{P \left( \frac{r}{n} \right)}{1 - \left(1 + \frac{r}{n}\right)^{-nt}}
   \]
2. Once we have the monthly payment, calculate the total payments made over the loan term by multiplying the monthly payment by the total number of payments $ n \times t $.
3. Subtract the loan principal from the total payments to find the total interest paid.

Let's calculate it!# Loan parameters for the given problem
P = 13000  # Loan amount
r = 0.06  # Annual interest rate
n = 12  # Number of payments per year
t = 5  # Loan term in years

# Calculate the monthly payment
monthly_payment = calculate_monthly_payment(P, r, n, t)

# Calculate the total amount paid over the life of the loan
total_payments = monthly_payment * n * t

# Calculate the total interest paid
total_interest = total_payments - P

monthly_payment, total_interestThe monthly payment for the loan would be approximately **$251.33**. Over the course of the loan, the total interest paid would be approximately **$2,079.59**.

Would you like further explanation or have any other questions?

### Related Questions:
1. What would the monthly payment be if the interest rate were reduced to 5%?
2. How does the total interest change if the loan term is shortened to 4 years?
3. What is the total amount repaid over the life of the loan?
4. How would a larger down payment impact the monthly payments?
5. If you made an extra payment of $500 once a year, how would that affect the total interest paid?
6. What would happen to the monthly payment if the loan term were extended to 6 years?
7. How does the loan payment formula change if payments are made quarterly instead of monthly?
8. What are the benefits of paying off the loan early?

**Tip**: Making extra payments toward your loan's principal can significantly reduce the total interest paid over time.

Learn how to calculate monthly payments and total interest for a car loan using the loan payment formula. Given a loan amount of $13,000, an annual interest rate of 6%, and a loan term of 5 years, find out the monthly payment and total interest paid over the loan term. Suitable for high school students studying finance or interest calculation.

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