You can afford a $400 per month car payment. You've found a 3 year loan at 4% interest. How big of a loan can you afford

To determine the maximum loan amount you can afford with a monthly payment of $400, a 3-year term, and a 4% annual interest rate, we'll use the formula for the present value of an ordinary annuity, which is used to calculate the loan principal based on regular payments:

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

Where:
- $ P $ is the loan principal (the amount you can borrow).
- $ PMT $ is the monthly payment, which is $400.
- $ r $ is the monthly interest rate (annual rate divided by 12).
- $ n $ is the total number of payments (loan term in months).

Given dataTo determine the maximum loan amount you can afford with a monthly payment of $400, a 3-year term, and a 4% annual interest rate, we'll use the formula for the present value of an ordinary annuity, which is used to calculate the loan principal based on regular payments:

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

Where:
- $ P $ is the loan principal (the amount you can borrow).
- $ PMT $ is the monthly payment, which is $400.
- $ r $ is the monthly interest rate (annual rate divided by 12).
- $ n $ is the total number of payments (loan term in months).

Given 
- Annual interest rate = 4%, so the monthly rate $ r = \frac{4\%}{12} = 0.003333 $ (or 0.0033 when rounded).
- Loan term = 3 years = 36 months
- Monthly payment $ PMT = 400 $

Let's plug these values into the formula to find the maximum loan amount $ P $.

\[
P = \frac{400 \times \left(1 - (1 + 0.003333)^{-36}\right)}{0.003333}
\] 

Calculating this will give the amount you can afford to borrow. Let's do this calculation.The maximum loan amount you can afford with a $400 monthly payment over a 3-year loan at a 4% annual interest rate is approximately **$13,548.31**.

Would you like more details or have any questions about this calculation?

Here are 5 related questions you might find helpful:
1. How would the loan amount change if the interest rate increased to 5%?
2. What would be the monthly payment for a 4-year loan at the same interest rate?
3. How much total interest will be paid over the 3-year loan period?
4. What is the impact of making an additional payment on the loan?
5. How does the loan amount change if payments are made bi-weekly instead of monthly?

**Tip:** Making additional payments towards the principal can significantly reduce the total interest paid over the life of the loan.

You can afford a $400 per month car payment. You've found a 3 year loan at 4% interest. How big of a loan can you afford?

Discover how to calculate the maximum loan amount you can afford with a $400 monthly payment on a 3-year loan at a 4% interest rate. This guide covers the formula for the present value of an ordinary annuity and provides a step-by-step solution for determining the loan principal. Suitable for high school students learning finance math.

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