You can afford a $450 per month car payment. You've found a 3 year loan at 3% interest. How big of a loan can you afford?

To determine how big of a loan you can afford, we need to use the formula for the present value of an ordinary annuity, since you're making monthly payments over a fixed period.

The formula for the present value of an annuity is:

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

Where:
- $PV$ is the present value (the loan amount),
- $P$ is the monthly payment ($450),
- $r$ is the monthly interest rate,
- $n$ is the total number of payments.

### Step-by-step:
1. **Monthly interest rate**: The annual interest rate is 3%, so the monthly interest rate is:

\[
r = \frac{3\%}{12} = \frac{0.03}{12} = 0.0025
\]

2. **Total number of payments**: Since the loan is for 3 years, with monthly payments, the total number of payments is:

\[
n = 3 \times 12 = 36
\]

3. **Plugging into the formula**:

\[
PV = 450 \times \frac{1 - (1 + 0.0025)^{-36}}{0.0025}
\]

Let me calculate this for you.The maximum loan you can afford with a $450 monthly payment over a 3-year loan at 3% interest is approximately **$15,474**.

Do you have any questions or need further details?

Here are some related questions you might find interesting:
1. How would a change in the interest rate affect the loan amount?
2. What would be the loan amount if the loan term was 5 years instead of 3?
3. How much total interest would you pay over the life of the loan?
4. How do bi-weekly payments instead of monthly affect the loan amount?
5. What if you made an extra payment each year? How much interest would you save?

**Tip:** Always consider the total cost of the loan (including interest) to understand the full financial impact of your payments.

You can afford a $450 per month car payment. You've found a 3-year loan at 3% interest. How big of a loan can you afford?

Learn how to calculate the loan amount you can afford with a $450 monthly payment and a 3% interest rate over 3 years. This step-by-step solution uses the present value of annuities formula, breaking down interest rate calculations and amortization concepts. Ideal for students in Grades 10-12.

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