You can afford a $250 per month car payment. You've found a 3 year loan at 7% interest. How big of a loan can you afford?

$


To find out how big of a loan you can afford, we can use the formula for the present value of an ordinary annuity:

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

Where:
- $ PV $ is the loan amount (present value),
- $ P $ is the monthly payment ($250),
- $ r $ is the monthly interest rate (annual interest rate divided by 12),
- $ n $ is the total number of payments (loan term in months).

Here are the values you provided:
- Monthly payment $ P = 250 $,
- Annual interest rate = 7%, so monthly interest rate $ r = \frac{7\%}{12} = 0.005833 $,
- Loan term = 3 years, which gives $ n = 3 \times 12 = 36 $ months.

Now let's calculate the loan amount $ PV $.The maximum loan amount you can afford, based on a $250 monthly payment over 3 years at 7% interest, is approximately **$8,096.62**.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How would the loan amount change if the interest rate were lower?
2. What if the loan term were extended to 5 years?
3. How do early repayments affect the total interest paid?
4. How much total interest would be paid over the life of the loan?
5. How would a higher monthly payment affect the loan amount?

**Tip:** Reducing the interest rate or increasing the loan term can make higher loan amounts more affordable!

You can afford a $250 per month car payment. You've found a 3-year loan at 7% interest. How big of a loan can you afford?

Learn how to calculate the maximum loan amount you can afford with a $250 monthly payment, a 3-year loan term, and a 7% annual interest rate. Using the present value of an ordinary annuity formula, this finance-related problem provides a step-by-step breakdown of the loan calculation process. Suitable for Grades 10-12.

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