A NOW account requires a minimum monthly balance of $500 if annual interest of 5 percent is to be earned monthly on its deposits.An account holder has maintained an average balance of $300 for the first nine months of the year and $800 for the last three months of the year.She has written an average of 20 checks a month and is not charged for these services.However, it costs the bank $0.02 to process each check. The bank would like to limit the average return (both explicit and implicit) earned by the account holder to 5 percent per year.How much should it charge for processing each check to this Account holder assuming that it will pay annual interest of 5 percent and minimum balances of $200 are maintained?
A)1 cent per check.
B)2 cent per check.
C)3 cent per check.
D)4 cent per check.
E)5 cent per check.

Question

Quizplus · Accepted Answer

To calculate the correct charge per check, we first determine the average balance for the year and the interest earned on it. The average balance is calculated as follows: $$ \text{Average balance} = \frac{(300 \times 9) + (800 \times 3)}{12} = \frac{2700 + 2400}{12} = \frac{5100}{12} = 425 $$ The interest earned at 5% annually on this average balance is: $$ \text{Interest} = 425 \times 0.05 = 21.25 $$ The bank incurs a cost of $0.02 per check for processing 20 checks a month over 12 months, which totals: $$ \text{Cost} = 20 \times 12 \times 0.02 = 4.8 $$ To limit the return to 5%, the bank must ensure the total return (interest plus the value of free services) does not exceed 5% of the average balance. The total value of services (including the cost of processing checks) is essentially the cost to the bank, which is $4.8. Since the interest paid is $21.25 and the cost of services is $4.8, the total return to the customer is: $$ \text{Total return} = 21.25 + 4.8 = 26.05 $$ However, to limit the return to 5%, the bank should aim for the total return to be equal to 5% of the average balance, which is: $$ \text{Desired return} = 425 \times 0.05 = 21.25 $$ Since the bank wants to limit the return to what is already being paid as interest, it should not provide any additional implicit return through free services. Therefore, the bank should charge for processing each check to cover the $4.8 cost, which is already being incurred. Since the bank is already incurring $4.8 without charging the customer, and the goal is to not exceed the 5% return (which is fully utilized by the interest payment), the bank should start charging for check processing to recover the $4.8 cost. However, the question asks how much more should be charged per check, assuming the bank wants to maintain the 5% return limit, and given the current setup, the bank is already meeting its goal by not exceeding the 5% return with the interest payment alone. The question's premise on charging more per check seems to aim at reducing the implicit return, but the calculation provided does not directly lead to a new charge per check based on the information given. The bank's goal is to not exceed a 5% return, which is met with the interest payment. The cost to the bank for processing checks is an additional factor that doesn't affect the calculation for charging per check based on the provided data and goal of limiting the return to 5%.

A NOW Account Requires a Minimum Monthly Balance of $500