You can afford a $300 per month car payment. You've found a 5 year loan at 6% interest. How big of a loan can you afford?

To calculate the size of the loan you can afford, we can use the formula for the present value of an ordinary annuity, which is often used to determine the principal amount of a loan given a fixed monthly payment, an interest rate, and a loan term.

### Given Information:
- Monthly payment ($PMT$) = $300
- Loan term = 5 years = 60 months
- Monthly interest rate ($r$) = Annual rate / 12 = 6% / 12 = 0.5% = 0.005

### Formula:
The formula for the present value of an ordinary annuity is:

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

where:
- $PV$ = Present value (the loan amount you can afford)
- $PMT$ = Monthly payment ($300)
- $r$ = Monthly interest rate (0.005)
- $n$ = Total number of payments (60)

Let's plug in the values to calculate the present value.The maximum loan amount you can afford with a $300 per month payment over 5 years at a 6% annual interest rate is approximately **$15,517.67**.

Would you like more details, or do you have any questions?

### Related Questions:
1. How would the loan amount change if the interest rate were 5% instead of 6%?
2. What would be the monthly payment for a loan amount of $20,000 under the same conditions?
3. How much total interest will you pay over the course of this loan?
4. How would a shorter loan term (e.g., 3 years) affect the maximum loan amount?
5. What is the impact of making extra payments on this loan?

**Tip:** When comparing loan offers, consider both the interest rate and the loan term to find the most affordable option.

Learn how to calculate the maximum loan amount you can afford with a $300 monthly car payment over a 5-year term at a 6% annual interest rate. This guide covers the present value of an ordinary annuity formula, loan amortization, and related financial concepts. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation