A NOW account requires a minimum balance of $750 for interest to be earned at an

Question

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.

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.

Explanation / Answer

a. What average return does the account holder earn on the account?

Interest earned on first $500 ($500 * 0 * 6 / 12)

$0

Interest earned on next $1000 ($1000 * .04 * 6 / 12)

$20

Fees earned on checks ($.05 - $.02) * 60 * 12

$21.6

Total interest earned ($20 + $21.6)

$41.6

Average balance maintained

$750

Average return ($41.6 / $750)

5.55%

b. What is the average return if the bank lowers the minimum balance to $400?

Interest earned on first $500 ($500 * .04 * 6 / 12)

$10

Interest earned on next $1000 ($1000 * .04 * 6 / 12)

$20

Fees earned on checks ($.05 - $.02) * 60 * 12

$21.6

Total interest earned ($10 + $20 + $21.6)

$51.6

Average balance maintained

$750

Average return ($51.6 / $750)

6.88%

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?

Interest earned on first $100 ($100 * .04 * 6 / 12)

$2

Interest earned on next $600 ($600 * .04 * 6 / 12)

$12

Fees earned on checks ($.05 - $.02) * 60 * 12

$21.6

Total interest earned ($2 + $12 + $21.6)

$35.6

Average balance maintained

$750

Average return ($35.6 / $750)

4.75%

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;

Total interest earned ($750 * .05)

$37.5

Thus fees earned on checks should be ($37.5 - $20)

$17.5

Subsidiary per check ($17.5 / 60*12)

$.0243

Thus bank increase per check fees ($.05 – $.0243)

$.0257

Interest earned on first $500 ($500 * 0 * 6 / 12)

$0

Interest earned on next $1000 ($1000 * .04 * 6 / 12)

$20

Fees earned on checks ($.05 - $.02) * 60 * 12

$21.6

Total interest earned ($20 + $21.6)

$41.6

Average balance maintained

$750

Average return ($41.6 / $750)

5.55%

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