Question

A bank made a loan and charged a 4 point loan fee. Later the banker sold the note at a 3 1/2 point discount and received a check for 69580. What was most nearly the face amount of the loan?

Answer 1

To find the face amount of the loan, subtract the loan fee and discount from the check received and solve for the unknown variable.

Step-by-step explanation:

To find the face amount of the loan, we need to calculate the original loan amount. Let's assume the face amount of the loan is x. The bank charged a 4 point loan fee, which is 4% of the face amount. So the loan fee charged is 0.04x. After that, the banker sold the note at a 3 1/2 point discount, which is 3.5% of the face amount. So the discount received is 0.035x. The check received is $69580, which is the face amount minus the loan fee and the discount, so we can write the equation: x - 0.04x - 0.035x = $69580. Simplifying the equation, we get 0.925x = $69580. Solving for x, we find that the face amount of the loan is approximately $75297.30.