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To solve this problem, we need to determine the maximum loan amount Cindy can afford, based on a monthly payment of $181, a loan period of 6 years, and an annual percentage rate (APR) of 3.5%.

This is a classic loan amortization problem, which can be solved using the formula for the present value of an annuity (used to calculate loan payments):

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

Where:
- $ P $ is the loan amount (what we need to find),
- $ R $ is the monthly payment, $181 in this case,
- $ r $ is the monthly interest rate (annual rate divided by 12),
- $ n $ is the total number of payments (loan term in months).

### Given values:
- $ R = 181 $,
- Annual interest rate = 3.5%, so $ r = \frac{0.035}{12} $,
- Loan term = 6 years, so $ n = 6 \times 12 = 72 $ months.

Now, I'll calculate the loan amount $ P $.The most expensive car loan that Cindy can afford, based on her monthly budget and the given terms, is approximately **$11,739**.

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

Here are 5 related questions you might find useful:
1. How does changing the interest rate affect the maximum loan amount?
2. What would happen if the loan term was extended to 7 or 8 years?
3. How can you calculate the monthly payment if you know the loan amount and interest rate?
4. How do extra payments on a loan affect the total interest paid?
5. What is the difference between fixed-rate and variable-rate loans?

**Tip:** When considering loans, always check the total interest you'll pay over time by comparing different loan terms and interest rates.

Cindy has a new job offer but will need a new car for the job. After planning a budget, they determine that they can afford to pay at most $181 per month for a 6-year car loan. If an annual percentage rate of 3.5% is available to finance the car loan, calculate the value of the most expensive car loan that Cindy can afford. Round to the nearest whole number.

Calculate the maximum car loan Cindy can afford with a $181 monthly payment over 6 years at a 3.5% annual interest rate. Learn how loan amortization works with step-by-step solutions using the annuity formula. Ideal for students in Grades 10-12.

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