You took out a car loan for a period of 3 years with 5.48% annual interest compounded monthly. Your monthly payment is $629 for 3 years. What was the amount of the loan? 

Round your answer to the nearest cent.

To find the loan amount, we can use the formula for the present value of an ordinary annuity:

\[
PV = \frac{PMT \times \left(1 - (1 + r)^{-n}\right)}{r}
\]

Where:
- $PV$ is the present value (loan amount),
- $PMT$ is the monthly payment (\$629),
- $r$ is the monthly interest rate,
- $n$ is the total number of payments.

### Step 1: Calculate the monthly interest rate
The annual interest rate is 5.48%, so the monthly interest rate is:

\[
r = \frac{5.48\%}{12} = \frac{0.0548}{12} = 0.0045667
\]

### Step 2: Calculate the total number of payments
The loan term is 3 years, so with monthly payments:

\[
n = 3 \times 12 = 36
\]

### Step 3: Plug the values into the formula
Now, substituting the values into the present value formula:

\[
PV = \frac{629 \times \left(1 - (1 + 0.0045667)^{-36}\right)}{0.0045667}
\]

I will calculate the result.The amount of the loan is approximately **$20,836.87**.

Would you like more details or have any questions about this calculation? 

Here are some related questions:
1. How does the interest rate impact the loan amount over time?
2. What would happen to the monthly payment if the loan term was extended?
3. How can changing the compounding frequency affect the loan's total cost?
4. What is the total interest paid over the life of the loan?
5. How would the loan amount change if the interest rate were reduced by 1%?

**Tip:** Always review the loan’s interest rate and payment terms carefully, as small differences in rates or periods can have a significant impact on the total cost of borrowing.

You took out a car loan for a period of 3 years with 5.48% annual interest compounded monthly. Your monthly payment is $629 for 3 years. What was the amount of the loan? Round your answer to the nearest cent.

Learn how to calculate the loan amount for a car loan with a 5.48% annual interest rate compounded monthly, using a $629 monthly payment for 3 years. This problem involves key finance concepts such as the present value of an annuity and compound interest. Suitable for Grades 11-12 and college-level finance.

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