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. What is the average return earned (both explicit and implicit) by the account holder over the full year?
A)2.98 percent.
B)3.48 percent.
C)4.28 percent.
D)4.79 percent.
E)5.35 percent.

Question

Quizplus · Accepted Answer

To calculate the average return earned by the account holder, we need to consider both the explicit interest earned and the implicit benefits from the free check-writing services.1. **Explicit Interest Earned:**   - The account earns 5% annual interest, but only if the minimum monthly balance of $500 is maintained.    - For the first 9 months, the average balance is $300, which is below the minimum, so no interest is earned during this period.   - For the last 3 months, the average balance is $800, which is above the minimum, so interest is earned on this balance.   - Annual interest for the last 3 months = $800 * 5% * (3/12) = $10.2. **Implicit Benefit from Free Check-Writing:**   - The account holder writes an average of 20 checks per month, for a total of 240 checks a year.   - The bank's cost to process each check is $0.02, so the total cost saved by the account holder = 240 checks * $0.02/check = $4.80.3. **Total Benefit (Explicit + Implicit):**   - Total explicit interest earned = $10.   - Total implicit benefit from free check-writing = $4.80.   - Total benefit = $10 + $4.80 = $14.80.4. **Average Return Earned:**   - The average balance over the year = (9 months * $300 + 3 months * $800) / 12 = $450.   - Average return = (Total benefit / Average balance) * 100 = ($14.80 / $450) * 100 ≈ 3.29%.However, the calculation above does not directly match any of the provided options, suggesting a need for reevaluation based on the options given. Given the options, the closest match or the intended calculation method might involve a different interpretation of how the average return is calculated or a simplification in the steps provided. The correct choice based on the options provided and assuming a potential misstep in the detailed calculation would be to reevaluate the explicit and implicit returns in the context of the options given. Since none of the calculations directly match the options and assuming a potential misinterpretation in the detailed steps, the correct answer based on the options and the typical approach to such problems would likely involve a reconsideration of the average balance or interest calculation method. The provided explanation aimed to break down the calculation step by step, but without matching the options, it suggests a need for recalibration based on the specific methodology expected in the question's context.

A NOW Account Requires a Minimum Monthly Balance of $500