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 $280 per month for a 6-year car loan. If an annual percentage rate of 2.0% 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.

To calculate the value of the most expensive car loan that Cindy can afford, we can use the formula for the present value of an annuity, which is commonly used to calculate loan payments. The formula is:

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

Where:
- $ PV $ is the present value (the loan amount).
- $ P $ is the monthly payment ($280 in this case).
- $ r $ is the monthly interest rate.
- $ n $ is the total number of payments (the number of months).

### Step 1: Determine the values for $ P $, $ r $, and $ n $
- $ P = 280 $
- Annual interest rate is 2.0%, so the monthly interest rate $ r = \frac{2.0\%}{12} = \frac{0.02}{12} = 0.001667 $.
- The loan term is 6 years, so the total number of months $ n = 6 \times 12 = 72 $.

### Step 2: Substitute the values into the formula

\[
PV = 280 \times \frac{1 - (1 + 0.001667)^{-72}}{0.001667}
\]

Now, let's calculate the value of $ PV $.The most expensive car loan that Cindy can afford, given a monthly payment of $280, a 6-year term, and a 2.0% annual interest rate, is approximately **$18,982**.

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

Here are 5 related questions you could explore:
1. How would the loan amount change if the interest rate were higher?
2. What is the total interest paid over the 6-year period?
3. How does the loan amount change if Cindy can only afford $250 per month?
4. What is the impact of choosing a shorter loan term, like 5 years?
5. How would the monthly payment change if Cindy wanted to borrow $20,000 instead?

**Tip:** When calculating loans, always consider how even small changes in the interest rate or term length affect the monthly payment and total cost.

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 $280 per month for a 6-year car loan. If an annual percentage rate of 2.0% 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.

Discover how to calculate the most expensive car loan Cindy can afford with a $280 monthly budget, a 6-year loan term, and a 2.0% APR. This problem explains the use of the present value of annuities formula to solve real-life financial questions. Perfect for Grades 11-12 students learning finance mathematics.

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