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To solve this problem, we need to calculate the loan amount you can borrow and the interest you would pay, given the following information:

- Monthly payment: $250
- Interest rate: 6.4% compounded monthly (0.064 / 12 per month)
- Loan term: 5 years (60 months)

### Step 1: Identify the formula

The formula for the present value of an annuity (which is used to calculate how much you can borrow) is:

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

Where:
- $PV$ = Present Value (the amount you can borrow)
- $P$ = Payment per period ($250)
- $r$ = Monthly interest rate (annual rate / 12)
- $n$ = Number of periods (number of months in 5 years)

### Step 2: Plug in the known values

1. **Monthly interest rate** $r = \frac{6.4\%}{12} = 0.064 / 12 = 0.0053333$
2. **Number of periods** $n = 5 \times 12 = 60$ months
3. **Monthly payment** $P = 250$

Now substitute these into the formula:

\[
PV = \frac{250(1 - (1 + 0.0053333)^{-60})}{0.0053333}
\]

### Step 3: Calculate the Present Value (loan amount)

Let me calculate this for you.The amount you are able to borrow is approximately **$12,807.81**.

### Step 4: Calculate the total interest paid

To find out how much interest you will pay over the 5 years, we first need to calculate the total amount of payments made and then subtract the loan amount (principal).

1. **Total payments** = Monthly payment $\times$ number of months
   \[
   \text{Total Payments} = 250 \times 60 = 15,000
   \]

2. **Interest paid** = Total payments - Loan amount
   \[
   \text{Interest Paid} = 15,000 - 12,807.81 = 2,192.19
   \]

Thus, the total interest you will pay is approximately **$2,192.19**.

Would you like more details or clarifications? 

Here are 5 related questions you might explore:
1. How would the loan amount change if the interest rate increased?
2. What happens if you reduce the loan term to 3 years instead of 5?
3. How can you calculate your monthly payment if you change the loan amount?
4. How does the total interest paid change with bi-weekly payments?
5. How would an additional down payment affect the loan?

**Tip:** Reducing the loan term significantly lowers the total interest you pay over time.

You want to buy a new car. You can afford payments of $250 per month and can borrow the money at an interest rate of 6.4% compounded monthly for 5 years. How much are you able to borrow? How much interest do you pay?

Calculate the amount you can borrow for a car with monthly payments of $250, an interest rate of 6.4% compounded monthly, and a loan term of 5 years. Learn how to determine the loan amount and total interest paid using the present value of annuity formula.

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