You can afford a $200 per month car payment. You've found a 3 year loan at 2% interest. How big of a loan can you afford?


To determine how large of a loan you can afford, we will calculate the **present value** of the loan, given that you can afford $200 per month, with a 3-year loan at 2% interest. 

We will use the formula for the **present value of an annuity**:

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

Where:
- $PV$ is the loan amount (the present value we are solving for),
- $P = 200$ is the monthly payment,
- $r = \frac{0.02}{12}$ is the monthly interest rate (annual interest rate divided by 12),
- $n = 3 \times 12 = 36$ is the total number of payments (months).

Now, let me calculate the result.The largest loan you can afford with a $200 per month payment over 3 years at 2% interest is approximately **$6,982.61**.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How would the loan amount change if the interest rate were higher, say 4%?
2. What would happen if the loan term were extended to 5 years?
3. How much total interest would you pay over the course of the loan?
4. What would your monthly payments be if you borrowed $10,000 instead?
5. What is the difference between simple interest and compound interest in loan calculations?

**Tip:** Always consider both the loan term and interest rate when calculating the affordability of a loan, as they significantly affect the monthly payment and total interest paid.

You can afford a $200 per month car payment. You've found a 3 year loan at 2% interest. How big of a loan can you afford?

Learn how to calculate the maximum loan amount you can afford with a $200 monthly car payment on a 3-year loan at 2% interest. This problem uses the Present Value of an Annuity formula to determine the loan size, covering important concepts in loan amortization and interest rates. Ideal for high school students (Grades 10-12).

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