https://file.aiquickdraw.com/mathbot/file/1730057993767j0bvffee.jpg

From the image, you are asked to determine how big of a loan you can afford if you can pay $350 per month, with a 4-year loan at 3% interest. Let's break it down step by step:

1. **Loan Details:**
   - Monthly payment ($ P $) = $350
   - Loan term ($ n $) = 4 years = 48 months
   - Annual interest rate ($ r $) = 3% per year, or $ 0.03 \div 12 $ per month = $ 0.0025 $ per month

2. **Loan Formula:**
   The formula to calculate the loan amount ($ L $) is derived from the formula for an installment loan:
   
   \[
   L = \frac{P \cdot \left(1 - (1 + r)^{-n}\right)}{r}
   \]
   
   Plugging in the values:
   \[
   L = \frac{350 \cdot \left(1 - (1 + 0.0025)^{-48}\right)}{0.0025}
   \]

3. **Calculation:**
   I'll compute the value for you.

\[
   L = \frac{350 \cdot \left(1 - (1 + 0.0025)^{-48}\right)}{0.0025}
\]

   Let's calculate it.

\[
  L \approx \frac{350 \cdot 0.1123}{0.0025} \approx 15,734.5
\]

So, you can afford a loan of approximately **$15,734.50**.

Would you like more details or clarifications on any part?

### Related Questions:
1. How does the interest rate affect the loan amount I can afford?
2. What would happen if I increased my monthly payment?
3. How would the loan change with a longer term, say 5 years?
4. How much interest would I end up paying over the life of the loan?
5. What would happen if I found a loan with a 2% interest rate instead?

**Tip:** Always compare loans using the **total interest paid** over the term, not just the monthly payments!

You can afford a $350 per month car payment. You've found a 4-year loan at 3% interest. How big of a loan can you afford?

Learn how to calculate the maximum loan amount you can afford with a $350 monthly payment over a 4-year term at 3% interest. This solution explains key concepts in loan calculations, including interest rates and monthly payments, suitable for students in Grades 10-12.

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