You want to buy a new car. You can afford payments of $500 per month and can borrow the money at an interest rate of 6.3% compounded monthly for 5 years.

How much are you able to borrow?

$

How much interest do you pay?

$

To determine how much you can borrow and the total interest paid, we can use the formula for the present value of an annuity, since the payments are fixed, and the interest is compounded monthly. The formula is:

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

Where:
- $ PV $ is the present value (amount you can borrow).
- $ P $ is the monthly payment ($500).
- $ r $ is the monthly interest rate (annual interest rate divided by 12).
- $ n $ is the total number of payments (5 years × 12 months/year = 60 payments).

### Step 1: Determine the monthly interest rate $ r $:
\[
r = \frac{6.3\%}{12} = \frac{0.063}{12} = 0.00525
\]

### Step 2: Plug the values into the formula:
\[
PV = 500 \times \frac{1 - (1 + 0.00525)^{-60}}{0.00525}
\]

Let me calculate that for you.The amount you are able to borrow is approximately **$25,677.10**.

### Step 3: Calculate the total interest paid:
The total interest paid can be determined by subtracting the borrowed amount from the total amount paid over the 5 years.

\[
\text{Total payments} = P \times n = 500 \times 60 = 30,000
\]
\[
\text{Total interest} = \text{Total payments} - \text{Amount borrowed}
\]

Let me calculate that for you.The total interest you will pay over 5 years is approximately **$4,322.90**.

### Summary:
- Amount you can borrow: **$25,677.10**
- Total interest paid: **$4,322.90**

Would you like more details on how this is calculated, or have any further questions?

Here are 5 related questions to explore:
1. How does a different interest rate affect the amount you can borrow?
2. What if you increase the monthly payment to $600?
3. How would the total interest change if the loan term is reduced to 3 years?
4. How does a bi-weekly payment plan compare to a monthly one?
5. How does making a larger initial payment affect the loan amount?

**Tip:** Always compare different loan terms and interest rates to minimize the total interest paid over time.

You want to buy a new car. You can afford payments of $500 per month and can borrow the money at an interest rate of 6.3% compounded monthly for 5 years. How much are you able to borrow? $ How much interest do you pay? $

Learn how to calculate the maximum loan amount and total interest paid based on a monthly payment of $500 over 5 years with a 6.3% interest rate compounded monthly. This problem involves concepts of finance, present value calculations, and compound interest. Suitable for high school students in Grades 10-12.

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