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?

Question

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?

Quizplus · Accepted Answer

Average return earned = implicit and explicit interest
11efbabc_e405_d54f_8e22_7bb8727477a5_TB1314_00 
Average annual return = [(11.25 + 10) + (4.80 - fee income)]/average monthly balance
 26.05 - (0.05 * 425) = fee income = $4.80
 Fee income = annual number of checks * fee per check
$4.80 = (12 F1F1F1S1F1F1F10 20)F1F1F1S1F1F1F10 fee per check $4.80/240 = 0.02.

A NOW Account Requires a Minimum Monthly Balance of $500