Use the following information to answer the question. A current deposit account requires a minimum balance of $500 if annual interest of 5 per cent 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 cheques a month and is not charged for these services. However, it costs the bank $0.02 to process each cheque.
The bank would like to limit the average return (both explicit and implicit) earned by the account holder to 5 per cent per year. How much should it charge for processing each check to this Account holder assuming that it will pay annual interest of 5 per cent and minimum balances of $200 are maintained?
A) 1 cent per cheque
B) 2 cents per cheque
C) 3 cents per cheque
D) 4 cents per cheque.

Question

Quizplus · Accepted Answer

To limit the average return earned by the account holder to 5 per cent per year, the bank needs to adjust the interest earned and the fees charged for processing cheques.

For the first nine months, the average balance of $300 is below the minimum balance required to earn interest, so there is no interest earned during this period. For the last three months, the average balance of $800 is above the minimum balance required to earn interest, so interest is earned at a rate of 5% annually or 0.4167% monthly.

To calculate the limit on implicit return, we need to first calculate the amount of interest earned and the cost of processing cheques:

Interest earned = ($800 x 0.4167% x 3) = $10
Cost of processing cheques = (20 x $0.02 x 12) = $4.80

Total implicit return = $10 - $4.80 = $5.20

To limit the implicit return to 5%, the bank needs to charge additional fees. We can calculate the maximum amount of fees that can be charged as follows:

Max fees = (Average balance x Annual interest rate) - Implicit return
Max fees = (($550 x 5%) - $5.20) / 12 = $2.21 / 12 = $0.184

Therefore, the bank should charge at least 2 cents per cheque to this account holder to limit the average return to 5% per year.

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