You can afford a $200 per month car payment. You've found a 4 year loan at 2.5% annual interest rate, compounded monthly. How big of a loan amount can you afford? (Enter numeric answers to 2 decimal places.)


To calculate the loan amount $ P $ you can afford, we will use the formula for the present value of an annuity:

\[
P = \frac{PMT \times \left( 1 - (1 + \frac{r}{n})^{-nt} \right)}{\frac{r}{n}}
\]

Where:
- $ PMT $ is the monthly payment ($200),
- $ r $ is the annual interest rate (2.5% or 0.025),
- $ n $ is the number of times the interest is compounded per year (12 for monthly),
- $ t $ is the duration of the loan in years (4 years).

Now, let's calculate the loan amount $ P $.The loan amount you can afford is approximately \$9,126.57.

Would you like further details or have any questions?

Here are 5 related questions:
1. How would the loan amount change if the interest rate were higher?
2. What would happen if you opted for a 5-year loan instead of 4 years?
3. How does compound interest differ from simple interest in loans?
4. How do extra payments impact the total interest paid on a loan?
5. What factors should be considered when choosing a loan term?

**Tip:** Lowering the interest rate or extending the loan term can increase the loan amount you can afford, but it may result in paying more interest over time.

You can afford a $200 per month car payment. You've found a 4 year loan at 2.5% annual interest rate, compounded monthly. How big of a loan amount can you afford? (Enter numeric answers to 2 decimal places.)

Discover how to calculate the loan amount you can afford based on a $200 monthly car payment with a 4-year loan at a 2.5% interest rate, compounded monthly. This problem involves present value of an annuity and compound interest calculations. Suitable for high school students in Grades 11-12.

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