Suppose that you borrow $11000 for four years at 6% toward the purchase of a car. Use PMT = P(r/n)/[1-(1+r/n)^-nt ]   to find the monthly payments and the total interest for the loan. 

To find the monthly payments and the total interest for the loan, we'll use the given formula:

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

where:
- $ P = 11000 $ (the principal amount)
- $ r = 0.06 $ (the annual interest rate as a decimal)
- $ n = 12 $ (the number of compounding periods per year, since payments are monthly)
- $ t = 4 $ (the duration of the loan in years)

Substituting these values into the formula, we get:

\[
\text{PMT} = 11000 \times \frac{\frac{0.06}{12}}{1 - \left(1 + \frac{0.06}{12}\right)^{-12 \times 4}}
\]

Let's calculate the monthly payments (PMT) and the total interest paid over the life of the loan.The monthly payments (PMT) for the loan are approximately **$258.34**, and the total interest paid over the life of the loan is approximately **$1400.10**.

### Further Questions:
1. How would the monthly payment change if the interest rate were 8% instead of 6%?
2. What would be the effect on the total interest paid if the loan term were extended to 5 years?
3. How much would you save in interest if you made an extra payment of $500 each year?
4. What would be the monthly payment if the principal amount borrowed were $15,000 instead?
5. How does changing from monthly to bi-weekly payments affect the total interest paid?

### Tip:
Always compare different loan terms and interest rates to find the most cost-effective borrowing option!

Suppose that you borrow $11000 for four years at 6% toward the purchase of a car. Use PMT = P(r/n)/[1-(1+r/n)^-nt ] to find the monthly payments and the total interest for the loan.

Calculate the monthly payments and total interest for a $11000 car loan at an interest rate of 6% over 4 years. This example uses the loan amortization formula to find a monthly payment of $258.34 and a total interest paid of $1400.10. Perfect for high school and college students learning about loan calculations.

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