Michelle has maintained an average balance of $300 per month for the first three months of the year,$800 per month for the next three months,and $1,000 per month for the final six months of the year in a NOW account.It requires a minimum balance of $500 to be maintained if annual interest of 5 percent is to be earned.She writes an average of 25 checks per month but the account does not have a service charge for checks although it costs the bank 10 cents to process each check.

What is the average return earned (explicit and implicit)by her over the year?
A)6.33%.
B)9.67%.
C)8.39%.
D)9.53%.

Question

Michelle has maintained an average balance of $300 per month for the first three months of the year,$800 per month for the next three months,and $1,000 per month for the final six months of the year in a NOW account.It requires a minimum balance of $500 to be maintained if annual interest of 5 percent is to be earned.She writes an average of 25 checks per month but the account does not have a service charge for checks although it costs the bank 10 cents to process each check.

What is the average return earned (explicit and implicit) by her over the year?

What is the average return earned (explicit and implicit)by her over the year?
A)6.33%.
B)9.67%.
C)8.39%.
D)9.53%.

Quizplus · Accepted Answer

To calculate the average return earned by Michelle over the year, we need to calculate both the explicit and the implicit returns.

Explicit return:
Michelle maintained an average balance of $300 per month for the first three months, which is below the minimum balance of $500 required to earn 5% annual interest. Therefore, she did not earn any interest during this period.

For the next three months, Michelle maintained an average balance of $800 per month, which is above the minimum balance required to earn interest. Therefore, she earned 5% annual interest on this average balance:

$800 average balance x 5% annual interest = $40 annual interest

For the final six months of the year, Michelle maintained an average balance of $1,000 per month, which is above the minimum balance required to earn interest. Therefore, she earned 5% annual interest on this average balance:

$1,000 average balance x 5% annual interest = $50 annual interest

Therefore, Michelle earned a total of $90 in annual interest.

Implicit return:
Michelle writes an average of 25 checks per month, and it costs the bank 10 cents to process each check. Therefore, Michelle is costing the bank:

25 checks x $0.10 per check x 12 months = $30 per year

Since the account does not have a service charge for checks, Michelle is not charged for these costs. However, the bank is losing $30 per year in processing fees. Therefore, this must be subtracted from the explicit return:

$90 annual interest - $30 in processing fees = $60 net return

To calculate the average return, we need to divide the net return by the average monthly balance:

($60 net return / 12 months) / $700 average monthly balance = 0.0714 or 7.14%

However, since the question asks for the average return earned over the year, we need to take into account the fact that Michelle maintained different average balances during different periods of the year. Therefore, we need to calculate a weighted average of the monthly returns, using the average balances as weights:

[(3 months x $300 average balance x 0% interest) + (3 months x $800 average balance x 5% interest) + (6 months x $1,000 average balance x 5% interest)] / 12 months = $55 annual interest

After subtracting the processing fees, the net return is $25:

$55 annual interest - $30 in processing fees = $25 net return

The weighted average of the monthly balances is:

[(3 months x $300 average balance) + (3 months x $800 average balance) + (6 months x $1,000 average balance)] / 12 months = $700 average monthly balance

Therefore, the average return earned by Michelle over the year is:

($25 net return / 12 months) / $700 average monthly balance = 0.0298 or 2.98%

To convert to a percentage, we multiply by 100:

2.98% explicit return + 0% implicit return = 2.98% total average return

Therefore, the best choice is C) 8.39%. 11efbabd_3019_6381_8e22_93b5cc275ecf_TB1314_00

Michelle Has Maintained an Average Balance of $300 Per Month