A couple with a newborn baby needs a new vehicle. They need to borrow $28,000.00 for 5 years at 4.4% compounded monthly. (Round all answers to 2 decimal places.)

What is the monthly payment amount? $
What is the unpaid balance after 11 months? $

During this time period, how much interest did they pay? $


To solve this problem, we'll use the formula for the monthly payment of a loan (amortized loan formula) and calculate the unpaid balance after 11 months. Then, we can determine how much interest has been paid up to that point.

### 1. **Monthly Payment Calculation**

The formula for the monthly payment on a loan is:

\[
M = \frac{P \cdot r(1 + r)^n}{(1 + r)^n - 1}
\]

Where:
- $ M $ is the monthly payment
- $ P $ is the loan amount ($28,000)
- $ r $ is the monthly interest rate (annual rate divided by 12)
- $ n $ is the total number of payments (number of months)

Given:
- Loan amount $ P = 28,000 $
- Annual interest rate = 4.4% = 0.044
- Monthly interest rate $ r = \frac{0.044}{12} $
- Loan term = 5 years = 60 months

Let's calculate the monthly payment $ M $.

### 2. **Unpaid Balance After 11 Months**

The unpaid balance $ B_k $ after $ k $ payments is calculated using:

\[
B_k = P \cdot (1 + r)^n - M \cdot \frac{(1 + r)^k - 1}{r}
\]

We will calculate the balance after $ k = 11 $ months.

### 3. **Total Interest Paid After 11 Months**

The interest paid after 11 months can be found by calculating the total payments made so far, subtracting the principal repaid from it, and whatever is left is the interest paid.

I’ll calculate each of these steps now.### Results:
1. **Monthly Payment**: The monthly payment is approximately **$520.73**.
2. **Unpaid Balance After 11 Months**: The unpaid balance after 11 months is approximately **$29,041.88**.
3. **Interest Paid After 11 Months**: The total interest paid during the first 11 months is approximately **$6,769.94**.

Would you like further details or explanations on any part of the calculation?

Here are 5 related questions to expand on this information:
1. How does the loan term affect the monthly payment amount?
2. What would the balance be if payments were made bi-weekly instead of monthly?
3. How would a higher interest rate change the total interest paid over the loan?
4. What is the total interest paid over the full 5-year term?
5. How much would the monthly payment be if the loan amount was $35,000 instead?

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

A couple with a newborn baby needs a new vehicle. They need to borrow $28,000.00 for 5 years at 4.4% compounded monthly. (Round all answers to 2 decimal places.) What is the monthly payment amount? What is the unpaid balance after 11 months? During this time period, how much interest did they pay?

Learn how to calculate the monthly payment, unpaid balance after 11 months, and total interest paid for a $28,000 vehicle loan at 4.4% compounded monthly for 5 years. Includes step-by-step application of the loan amortization and compound interest formulas. Suitable for high school or college students.

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