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To find the size of the loan you can afford, we can use the formula for calculating the loan amount for an installment loan, given the monthly payment, interest rate, and term. The formula is:

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

Where:
- $ P $ is the loan amount (principal)
- $ M $ is the monthly payment ($350 in this case)
- $ r $ is the monthly interest rate (annual rate divided by 12), which is $ \frac{6\%}{12} = 0.005 $
- $ n $ is the total number of payments (4 years × 12 months = 48 payments)

Let's plug in the values:

- Monthly payment, $ M $ = $350
- Monthly interest rate, $ r $ = 0.005
- Total number of payments, $ n $ = 48

The loan amount is calculated as:

\[
P = \frac{350 \times (1 - (1 + 0.005)^{-48})}{0.005}
\]

Let's calculate this step by step.The maximum loan you can afford, based on a $350 monthly payment over 4 years at a 6% annual interest rate, is approximately $14,903.11.

Would you like a more detailed explanation, or do you have any questions?

Here are some related questions to consider:
1. What would happen to the loan amount if the interest rate were lower?
2. How would a longer loan term affect the amount you could borrow?
3. What is the impact of making a larger monthly payment on the loan amount?
4. How does compound interest affect loan calculations compared to simple interest?
5. What are the benefits and risks of financing a car through a loan versus paying in cash?

**Tip:** When calculating loan payments, always double-check if the interest is compounded monthly or annually, as it significantly affects the calculation.

You can afford a $350 per month car payment. You’ve found a 4-year loan at 6% interest. How big of a loan can you afford?

Learn how to calculate the loan amount you can afford based on a $350 monthly payment over 4 years with a 6% annual interest rate. This problem involves key financial concepts such as installment loans and compound interest calculations, suitable for high school students.

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