Question

You can afford a $ month car payment with a 4-year loan at 5% interest. How big of a loan can you afford?

Answer 1

You can afford a car loan of approximately $23,982.

Step-by-step explanation:

To determine the affordable car loan amount, you can use the loan payment formula:

`\[ P = (A \cdot r \cdot (1 + r)^n)/((1 + r)^n - 1) \]`

where:

- ( P ) is the monthly payment,

- ( A ) is the loan amount,

- ( r ) is the monthly interest rate (annual rate divided by 12),

- ( n \) is the total number of payments (loan term in years multiplied by 12).

Rearranging the formula to solve for ( A ), you get:

`\[ A = (P \cdot ((1 + r)^n - 1))/(r \cdot (1 + r)^n) \]`

Given that you can afford a $ monthly car payment with a 4-year loan at 5% interest, you plug in the values:

`\[ A = (\$)/((0.05)/(12) \cdot (1 + (0.05)/(12))^(4 \cdot 12) - 1) \]`

After evaluating this expression, you find that \
`/( A \approx \$23,982 \)).` Therefore, you can afford a car loan of approximately $23,982.

This calculation ensures that the monthly payment is within your budget, considering the interest rate and the loan term. It's crucial to assess your financial situation and choose a loan that aligns with your ability to make consistent payments without straining your budget.