Brooke bought a new car for $26,000
. She paid a 20%
 down payment and financed the remaining balance for 36
 months with an APR of 4.5%
. Assuming she made monthly payments, determine the total cost of Brooke's car. Round your answer to the nearest cent, if necessary.

To calculate the total cost of Brooke's car, we need to break it down into the following steps:

### 1. **Calculate the down payment:**
Since the down payment is 20% of the car's price, we can compute it as:
\[
\text{Down Payment} = 0.20 \times 26,000 = 5,200
\]

### 2. **Determine the amount to be financed:**
The amount Brooke financed is the price of the car minus the down payment:
\[
\text{Financed Amount} = 26,000 - 5,200 = 20,800
\]

### 3. **Calculate the monthly payment using the loan formula:**

The formula for monthly payments on an amortized loan is:
\[
M = P \frac{r(1 + r)^n}{(1 + r)^n - 1}
\]
Where:
- $ M $ = monthly payment
- $ P $ = principal (financed amount), which is $20,800
- $ r $ = monthly interest rate (APR divided by 12)
- $ n $ = number of payments (36 months)

#### Step 1: Convert the APR to a monthly interest rate:
\[
r = \frac{4.5\%}{12} = 0.045 / 12 = 0.00375
\]

#### Step 2: Plug the values into the formula:
\[
M = 20800 \times \frac{0.00375(1 + 0.00375)^{36}}{(1 + 0.00375)^{36} - 1}
\]

Now, calculating the monthly payment $ M $:
\[
M \approx 20800 \times \frac{0.00375(1.00375)^{36}}{(1.00375)^{36} - 1}
\]
\[
M \approx 20800 \times \frac{0.00375 \times 1.1448}{1.1448 - 1}
\]
\[
M \approx 20800 \times \frac{0.004293}{0.1448} \approx 20800 \times 0.02964
\]
\[
M \approx 616.52
\]

### 4. **Calculate the total payments over 36 months:**
\[
\text{Total Payments} = 616.52 \times 36 = 22,194.72
\]

### 5. **Determine the total cost of the car:**
The total cost includes both the down payment and the total financed payments:
\[
\text{Total Cost} = 5,200 + 22,194.72 = 27,394.72
\]

### Final Answer:
The total cost of Brooke's car is **$27,394.72**.

---

Would you like any more details or clarifications?

Here are some follow-up questions to consider:
1. How would the monthly payment change if the APR increased to 5%?
2. What would happen to the total cost if the loan term was 48 months instead of 36 months?
3. How much would Brooke save in interest by paying off the loan in 24 months instead of 36 months?
4. What is the total interest paid over the 36-month loan period?
5. How would the monthly payment change if Brooke had financed only $15,000?

**Tip**: When comparing loans, always look at both the APR and the loan term to understand the total cost of the loan.

Brooke bought a new car for $26,000. She paid a 20% down payment and financed the remaining balance for 36 months with an APR of 4.5%. Assuming she made monthly payments, determine the total cost of Brooke's car. Round your answer to the nearest cent, if necessary.

Learn how to calculate the total cost of a car purchased for $26,000 with a 20% down payment and financed over 36 months with a 4.5% APR. This step-by-step solution covers key concepts such as interest rates, loan amortization, and monthly payments. Suitable for students in Grades 9-12.

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