You can afford a $300 per month car payment. You've found a 3 year loan at 5% interest. How big of a loan can you afford?


To determine the size of the loan you can afford, we'll use the formula for the present value of an ordinary annuity. This is because you're making monthly payments on a loan.

The formula is:

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

Where:
- $ PV $ is the loan amount (the present value).
- $ P $ is the monthly payment ($300).
- $ r $ is the monthly interest rate (annual interest rate divided by 12).
- $ n $ is the total number of payments (loan term in months).

### Given:
- $ P = 300 $
- Annual interest rate = 5%, so monthly interest rate $ r = \frac{5}{100} \div 12 = 0.004167 $
- Loan term = 3 years, so $ n = 3 \times 12 = 36 $ months.

Let's calculate the loan amount:

\[
PV = 300 \times \frac{1 - (1 + 0.004167)^{-36}}{0.004167}
\]

I'll compute this for you.The maximum loan you can afford, given a $300 monthly payment over a 3-year period at 5% interest, is approximately **$10,009.71**.

Would you like further explanation, or do you have any other questions?

Here are some related questions you might find useful:
1. How do different loan terms affect the total loan amount?
2. What happens to the loan amount if the interest rate increases to 6%?
3. How much would the total interest paid be over the life of this loan?
4. What is the difference between an ordinary annuity and an annuity due in terms of loan payments?
5. How can I calculate the total cost of the loan including interest?

**Tip:** Always check if the loan includes additional fees, as they can affect your overall cost and payments.

You can afford a $300 per month car payment. You've found a 3 year loan at 5% interest. How big of a loan can you afford?

Find out how to calculate the maximum loan you can afford with a $300 monthly payment, 5% interest, and a 3-year loan term. This problem uses the present value of an annuity formula to determine a loan size of approximately $10,009.71, covering key concepts like annuities and interest rates.

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