Naomi is looking to buy a car and the she qualified for a 4-year loan from a bank offering an annual interest rate of 4.5%, compounded monthly Using the formula below, determine the maximum amount Naomi can borrow, *to the nearest dollar*, if the highest monthly payment she can afford is dollar sign, 500$500.

To determine the maximum amount Naomi can borrow for a 4-year car loan with an annual interest rate of 4.5%, compounded monthly, and a maximum monthly payment of $500, we can use the same loan formula:

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

Where:
- $ M $ is the monthly payment ($500 in this case),
- $ P $ is the principal amount (the amount she can borrow),
- $ r $ is the monthly interest rate,
- $ n $ is the total number of payments.

### Given:
- Annual interest rate ($ r_{annual} $) = 4.5% = 0.045
- Monthly interest rate ($ r $) = $ \frac{0.045}{12} $
- Number of years = 4
- Number of payments ($ n $) = 4 years * 12 months/year = 48

### Rearranging the formula to solve for $ P $:

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

Now, I'll calculate this for you.The maximum amount Naomi can borrow, to the nearest dollar, is **$21,926**.

Would you like more details or have any other questions?

Here are 5 related questions:
1. What would the maximum loan amount be if Naomi could afford $600 per month?
2. How much total interest will Naomi pay over the 4 years?
3. What would happen to the loan amount if the interest rate were reduced to 3.5%?
4. How does the loan term affect the maximum loan amount Naomi can borrow?
5. What would Naomi's monthly payment be if she borrowed $25,000 instead?

**Tip:** Always compare different loan offers, as a slight difference in the interest rate can significantly impact the total amount you pay over time.

Learn how to calculate the maximum loan amount Naomi can borrow for a 4-year car loan with a 4.5% annual interest rate, compounded monthly, given a maximum monthly payment of $500. Get detailed calculations and understand the impact of interest rates on loan amounts.

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