You want to buy a new car. You can afford payments of $325 per month and can borrow the money at an interest rate of 3% compounded monthly for 5 years.

How much are you able to borrow?

$

How much interest do you pay?

$

This problem involves calculating the present value of an annuity, which represents the loan you can afford given the monthly payments, interest rate, and loan term. 

### 1. **Loan Amount (Present Value of Annuity) Calculation:**
We use the present value formula for an ordinary annuity:

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

Where:
- $ P $ = monthly payment = \$325
- $ r $ = monthly interest rate = $\frac{3\%}{12} = 0.0025$
- $ n $ = total number of payments = $5 \, \text{years} \times 12 = 60$ months

Let's calculate the present value (loan amount).

### 2. **Total Interest Paid:**
Once we have the loan amount, we can calculate the total interest by comparing the total of all payments made to the initial loan:

\[
\text{Total Interest} = (P \times n) - PV
\]

I'll calculate this now.You are able to borrow **$18,087.02**.

The total interest you would pay over the 5 years is **$1,412.98**.

Would you like further details on the calculation or have any questions?

Here are 5 related questions you might find useful:
1. What would happen if you could make a higher monthly payment?
2. How would the loan amount change with a higher interest rate?
3. How does compounding frequency affect the loan cost?
4. How much would you save by making extra payments?
5. What if you chose a 7-year loan instead?

**Tip:** Paying extra towards your principal each month can significantly reduce the total interest paid over the life of a loan.

You want to buy a new car. You can afford payments of $325 per month and can borrow the money at an interest rate of 3% compounded monthly for 5 years. How much are you able to borrow? How much interest do you pay?

Learn how to calculate the loan amount and total interest when making monthly payments of $325 at an interest rate of 3% compounded monthly for 5 years. This problem covers key financial concepts like the present value of an annuity and compound interest.

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