Question

An MMDA account has a minimum balance requirement of $1,000 and the depositor can have a maximum of 3 checks or transfers from the account each month. The bank pays 5.25 percent interest on the entire account balance but it costs $0.12 to process each check or transfer. There is also a monthly cost for statements and other account maintenance of $2.15. The bank does charge an annual account fee of $12.00 each January. Assume that the customer writes 3 checks each month and keeps an average balance of $3,000.

a. What explicit interest does the account holder earn each year?
b. What is the implicit interest that the bank absorbs each year?
c. What is the average annual return to the customer each year?

Answer 1

The account holder earns an explicit interest of $157.50 annually, absorbs implicit interest costs of $42.12, resulting in an average annual return of 3.846%.

Step-by-step explanation:

To calculate the explicit interest the account holder earns each year, we must look at the interest rate applied to the average balance. With a 5.25 percent interest rate on an average balance of $3,000, the calculation for annual explicit interest is as follows:

Explicit Interest = Average Balance × Interest Rate = $3,000 × 0.0525 = $157.50.

The implicit interest that the bank absorbs each year includes the costs of processing checks and the monthly and annual fees. Since there are 3 checks per month at $0.12 per check, 12 months in a year, a monthly cost of $2.15, and an annual fee of $12, the total costs are calculated:

Cost per check = 3 checks × $0.12 × 12 months = $4.32

Monthly maintenance cost = $2.15 × 12 months = $25.80

Total costs = Cost per check + Monthly maintenance cost + Annual fee = $4.32 + $25.80 + $12 = $42.12

The total implicit interest is the total costs subtracted from the explicit interest, $157.50 - $42.12 = $115.38.

To find the average annual return to the customer, we subtract the total costs from the explicit interest earned and divide by the average balance, then multiply by 100 to get a percentage:

Average Annual Return (%) = ((Explicit Interest - Total Costs) / Average Balance) × 100 = (($157.50 - $42.12) / $3,000) × 100 = 3.846%.