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

$


To determine how big of a loan you can afford with a monthly payment of $300, a 5-year loan term, and 3% annual interest, we can use the formula for the present value of an annuity:

\[
P = \dfrac{M \cdot (1 - (1 + r)^{-n})}{r}
\]

Where:
- $P$ is the loan amount (what we are solving for),
- $M$ is the monthly payment ($300),
- $r$ is the monthly interest rate (annual interest rate divided by 12, so $0.03/12 = 0.0025$),
- $n$ is the total number of payments (5 years × 12 months = 60 months).

Let’s calculate this.

\[
P = \dfrac{300 \cdot (1 - (1 + 0.0025)^{-60})}{0.0025}
\]

I'll compute this value.It seems there was an issue with the calculation. I'll walk through it manually:

First, calculate the monthly interest rate:
\[
r = \dfrac{0.03}{12} = 0.0025
\]

Next, calculate $(1 + r)^{-n}$, where $n = 60$ and $r = 0.0025$:
\[
(1 + 0.0025)^{-60} = 1.0025^{-60} \approx 0.860707976
\]

Now, substitute these into the formula for $P$:
\[
P = \dfrac{300 \cdot (1 - 0.860707976)}{0.0025} = \dfrac{300 \cdot 0.139292024}{0.0025} \approx \dfrac{41.7876072}{0.0025} \approx 16,715.04
\]

So, the loan you can afford is approximately **$16,715.04**.

Would you like more details or explanations? Here are 5 related questions to consider:

1. How does increasing the interest rate affect the loan amount you can afford?
2. What happens if you decrease the loan term to 3 years instead of 5 years?
3. How would a higher monthly payment, say $400, affect the loan you can take?
4. How can you calculate the total interest paid over the life of the loan?
5. What if the interest rate were compounded daily instead of monthly?

**Tip:** Always consider the total cost of the loan, not just the monthly payments, to fully understand your financial commitment.

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

Discover how to calculate the loan amount you can afford with a $300 monthly payment, 3% interest rate, and a 5-year term using the present value of an annuity formula. This detailed guide is perfect for high school students learning finance concepts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation