A NOW account requires a minimum balance of $750 for interest to be earned at an annual rate of 4 percent. An account holder has maintained an average balance of $500 for the first six months and $1,000 for the remaining six months. The account holder writes an average of 60 checks per month and pays $0.02 per check, although it costs the bank $0.05 to clear a check. Required:
a. What average return does the account holder earn on the account?
b. What is the average return if the bank lowers the minimum balance to $400?
c. What is the average return if the bank pays interest only on the amount in excess of $400? Assume that the minimum required balance is $400.
d. How much should the bank increase its check fee to the account holder to ensure that the average interest it pays on this account is 5 percent? Assume that the minimum required balance is $750.

a. Average return =  5.55%

b. Average return = 6.88%

c. Average return = 4.75%

d. Bank increase per check fees = $.0257

Explanation:

a.)

Interest earned on first $500 = $500×0×6 / 12 = $0

Interest earned on next $1000 = $1000×0.04×6 / 12=  $20

Now,

Fees earned on checks = ($.05 - $.02)×60×12 =  $21.6

So,

Total interest earned = $20 + $21.6 = $41.6

Given,

Average balance maintained  = $750

So,

Average return = $41.6 / $750 =  5.55%

b.)

Interest earned on first $500 = $500×0.04×6 / 12  = $10

Interest earned on next $1000 = $1000×0.04×6 / 12  = $20

Now,

Fees earned on checks = ($.05 - $.02)×60×12  = $21.6

So,

Total interest earned = $10 + $20 + $21.6 = $51.6

Given that,

Average balance maintained  = $750

So,

Average return = $51.6 / $750 = 6.88%

c.)

Interest earned on first $100 = $100×0.04×6 / 12 = $2

Interest earned on next $600 = $600×0.04×6 / 12 = $12

Now,

Fees earned on checks = ($.05 - $.02)×60×12  = $21.6

So,

Total interest earned = $2 + $12 + $21.6 = $35.6

Given that,

Average balance maintained = $750

So,

Average return = $35.6 / $750 = 4.75%

d.)

Total interest earned = $750×0.05 = $37.5

So,

fees earned on checks = $37.5 - $20 = $17.5

Subsidiary per check = $17.5 / 60×12 = $.0243

So,

Bank increase per check fees = $.05 – $.0243 = $.0257

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