Questions: You can afford a 450 per month car payment. You've found a 5 year loan at 2% interest. How big of a loan can you afford?

Transcript text: You can afford a $\$ 450$ per month car payment. You've found a 5 year loan at $2 \%$ interest. How big of a loan can you afford?

Solution

Solution Steps

Step 1: Identify the Parameters

The fixed monthly payment (PMT) is $450, the annual interest rate (r) is 2%, and the loan duration (n) is 60 months.

Step 2: Apply the Present Value of Annuity Formula

The formula to calculate the maximum loan amount (principal) that can be afforded is: \[ P = PMT \times \left( \frac{1 - (1 + r/12)^{-n}}{r/12} \right) \] Where:

$P$ is the principal amount of the loan.
$PMT$ is the fixed monthly payment.
$r$ is the annual interest rate (as a decimal).
$n$ is the total number of payments (loan duration in months).
$r/12$ adjusts the annual interest rate to a monthly rate.
$(1 + r/12)^{-n}$ calculates the discount factor for the annuity.

Step 3: Perform the Calculation

Substituting the given values into the formula, we get: \[ P = 450 \times \left( \frac{1 - (1 + 0.02/12)^{-60}}{0.02/12} \right) \] This simplifies to a maximum loan amount (principal) of $25673.56.

Final Answer:

The maximum loan amount that can be afforded with a fixed monthly payment of $450, an annual interest rate of 2%, and a loan duration of 60 months is $25673.56.

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

Next >

Thank you for your feedback.

Copied!