Suppose that you decide to borrow $15,000 for a new car. You can select one of the following loans, each requiring regular monthly payments.Installment Loan A: three-year loan at 5.1 %Installment Loan B: five-year loan at 6.4% Use PMT = P(r/n)/[1-1+r/n)^-nt ] What is the monthly payment for loan A?

To calculate the monthly payment for Installment Loan A using the provided formula, we will use the following dataTo calculate the monthly payment for Installment Loan A using the provided formula, we will use the following 

- **Loan Amount (P)** = $15,000
- **Annual Interest Rate (r)** = 5.1% = 0.051
- **Loan Duration (t)** = 3 years
- **Number of Payments per Year (n)** = 12 (monthly payments)

The formula for the monthly payment (PMT) is given by:

\[
\text{PMT} = \frac{P \cdot \left(\frac{r}{n}\right)}{1 - \left(1 + \frac{r}{n}\right)^{-nt}}
\]

### Substituting the values:

- $ P = 15,000 $
- $ r = 0.051 $
- $ n = 12 $
- $ t = 3 $

Now, let's calculate the monthly payment.The monthly payment for Installment Loan A (a 3-year loan at 5.1% interest) would be approximately **$450.24**.

Would you like to know more details or have any other questions? 

Here are five related questions for further exploration:

1. What would be the total interest paid over the course of Loan A?
2. How does the monthly payment compare for Loan B?
3. What happens if you make additional payments toward the principal on Loan A?
4. How does a higher interest rate affect your monthly payment and total interest paid?
5. How would a different loan term (e.g., 4 years instead of 3) affect your monthly payment?

**Tip:** Making extra payments toward the principal can significantly reduce the total interest paid over the life of a loan.

Suppose that you decide to borrow $15,000 for a new car. You can select one of the following loans, each requiring regular monthly payments. Installment Loan A: three-year loan at 5.1% Installment Loan B: five-year loan at 6.4%. Use PMT = P(r/n)/[1-1+r/n)^-nt ]. What is the monthly payment for loan A?

Learn how to calculate the monthly payment for a $15,000 car loan with a 3-year term at 5.1% interest using the loan amortization formula. This detailed guide is suitable for students in Grades 10-12, covering key concepts in finance mathematics.

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