Hello, I hope someone can help me with the question below, since I am completely stuck.
One day, a bank receives $5000 deposit on which they are going to pay 2% per year.
Same day, a student wants to take out a loan of $5000. The bank tells them that it costs $100 to process the loan in terms of service, time taken, cost of sending out monthly statements. The student wants to repay the loan in a year. What is the minimum interest rate the bank must charge the student to break even on this transaction?
So I tried using the Break even point equation, but I am confused as to what the variable cost is. E.g.
BEP = Fixed Cost/ (Price- Variable Cost)
I am so confused. Any help is appreciated.
To find the minimum interest rate the bank must charge the student to break even on this transaction, we can use the concept of break-even analysis.
In this scenario, the fixed cost is the $100 processing fee charged by the bank, as it does not change regardless of the interest rate charged. The price is the loan amount of $5000, and the variable cost represents the interest paid by the student.
Since the bank wants to break even, the revenue from the loan should cover both the fixed cost and the variable cost. The revenue in this case is the interest earned on the deposit.
To calculate the variable cost, we need to find the amount of interest the student must pay on the loan. The interest is calculated by multiplying the loan amount by the interest rate and the loan duration. However, we do not know the interest rate yet.
Let's break this down step by step:
Step 1: Calculate the variable cost (interest paid by the student):
Variable Cost = Loan Amount * Interest Rate * Loan Duration
Step 2: Calculate the revenue (interest earned by the bank):
Revenue = Deposit Amount * Interest Rate
Step 3: Set up the break-even equation:
Revenue - Variable Cost = Fixed Cost
Substituting the variables with the respective values:
Deposit Amount * Interest Rate - Loan Amount * Interest Rate * Loan Duration = Fixed Cost
Step 4: Solve for the interest rate:
Interest Rate = Fixed Cost / (Deposit Amount - Loan Amount * Loan Duration)
Inserting the values from the problem:
Interest Rate = $100 / ($5000 - $5000 * 1)
Simplifying this equation:
Interest Rate = 0.02 or 2%
So, the bank must charge a minimum interest rate of 2% to break even on this transaction.