Nora can afford monthly car payments of $400. If she is offered a 5-year amortized loan at 5%, what is the most expensive car that she can afford? Round to the nearest cent.

To find the most expensive car Nora can afford, we need to calculate the present value of a loan that has monthly payments of $400, over 5 years, with an interest rate of 5% per year. We can use the formula for the present value of an amortized loan:

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

Where:
- $ PV $ is the present value (the loan amount, or price of the car).
- $ P $ is the monthly payment ($400).
- $ r $ is the monthly interest rate (annual rate of 5% divided by 12 months).
- $ n $ is the total number of payments (5 years × 12 months per year).

### Step 1: Calculate the monthly interest rate
\[
r = \frac{5\%}{12} = \frac{0.05}{12} = 0.004167
\]

### Step 2: Calculate the total number of payments
\[
n = 5 \times 12 = 60 \text{ months}
\]

### Step 3: Plug values into the present value formula
\[
PV = 400 \times \frac{1 - (1 + 0.004167)^{-60}}{0.004167}
\]

Now, I will compute this value.The most expensive car that Nora can afford is approximately \$21,196.28.

Would you like more details or have any questions?

Here are five related questions you might find interesting:
1. How does the loan term affect the maximum car price Nora can afford?
2. What happens if the interest rate increases to 6%?
3. How much interest will Nora pay over the course of the loan?
4. What is the formula for calculating the monthly payment if she knows the car price?
5. How does making a down payment affect the loan amount?

**Tip:** When comparing loans, always look at the annual percentage rate (APR) to understand the true cost of borrowing.

Discover how to calculate the most expensive car Nora can afford with a 5-year loan at 5% interest and monthly payments of $400. This solution covers amortization concepts, present value formulas, and interest rate calculations, ideal for advanced high school or college-level students.

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