Question

Samuel wants to purchase a car. He reviewed his budget and can comfortably afford a car payment of $575 per month. He has good credit and anticipated being able to secure a 5-year loan at 2.5% interest. How much car loan can Samuel get for the $575 payment?

a) $30,000
b) $33,000
c) $35,000
d) $40,000

Answer 1

b) $33,000

Samuel can get a car loan amount of approximately $33,480 for a monthly payment of $575.

Step-by-step explanation:

To determine how much car loan Samuel can get for a monthly payment of $575, we need to calculate the loan amount that will result in this payment. Since Samuel anticipates being able to secure a 5-year loan at a 2.5% interest rate, we can use an amortization formula to find the loan amount. The formula is: Loan Amount = Payment / (Interest Rate * (1 + 1/((1 + Interest Rate)^(Loan Term * Number of Payments per Year)) - 1)). Plugging in the values, we get: Loan Amount = 575 / (0.025 * (1 + 1/((1 + 0.025)^(5 * 12)) - 1)). Evaluating this expression, we find that Samuel can get a car loan amount of approximately $33,480.