Question

A bank's cost to issue a loan, in dollars, isc = 200 + 0.03b, where b is the amount of the loan. If the bank's revenue from the loan is r = 0.07b, then what are the possible loan amounts that the bank can offer and have the revenue be greater than the cost?

Answer 1

The bank's revenue from a loan will be greater than the cost of issuing the loan if the amount of the loan is over $5,000; this is found by setting the revenue formula, 0.07b, greater than the cost formula, 200 + 0.03b, and solving for b.

Step-by-step explanation:

To determine the possible loan amounts that result in the bank's revenue being greater than the bank's cost, we set up an inequality where the revenue (r) is greater than the cost (c).

The cost to issue a loan, c, is given by the formula c = 200 + 0.03b, and the revenue from the loan, r, is given by r = 0.07b.

Setting up the inequality:

0.07b > 200 + 0.03b
In order to solve for b, we subtract 0.03b from both sides of the inequality:
0.04b > 200
Now, dividing both sides by 0.04 gives us:
b > 5000

Therefore, for the bank's revenue from the loan to be greater than the cost of issuing the loan, the amount of the loan, b, must be greater than $5,000.