Question

A bank's cost to issue a loan is

c=200+0.03b, where b is the loan amount. If the revenue is r=0.07b, what are the possible loan amounts for profit?
A) b > $1000
B) b > $2000
C) b > $3000
D) b > $4000

Answer 1

By setting up an inequality to compare the bank's cost of issuing a loan to the revenue from the loan, we found that for the bank to make a profit, the loan amount must be greater than $5000, which means none of the provided options are correct.

Step-by-step explanation:

To determine the possible loan amounts for profit, we need to compare the bank's cost of issuing a loan to the revenue from the loan.

The bank's cost, c, is given by c = 200 + 0.03b, and the revenue, r, is given by r = 0.07b. Profit occurs when revenue exceeds cost, so we need to find when r > c.

Setting up the inequality:

• 0.07b > 200 + 0.03b

Subtract 0.03b from both sides:

• 0.04b > 200

Divide both sides by 0.04:

• b > 5000

Therefore, the possible loan amounts for profit are when b > $5000. None of the options are correct since they don't match this answer.