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Jill has not been able to maintain the \(\$ 1,000\) minimum balance required to avoid fees on her checking account. She wants to switch to a different account with a fee of \(\$ 0.20\) per check and a \(\$ 12.50\) monthly maintenance fill wants to estimate the fees for her new account. Below is a summary of the checks she has written from May to August. $$\begin{array}{|c|c|}\hline & {\text { Number of }} {\text { Checks on }}\\\ \text { Month } & {\text { Statement }} \\ \hline\text { May } & {14} \\\ \hline \text { June } & {19} \\ \hline {\text { July }} & {23} \\\ \hline{\text { August }} & {24} \\ \hline\end{array}$$ a. What is the mean number of checks Jill wrote per month during the last four months? b. Based on the mean, estimate how much Jill expects to pay in per-check fees each month after she switches to the new account. c. Estimate the total monthly fees Jill will pay each month for the new checking account.

Step by step solution

01

Calculate the Mean Number of Checks

Calculate the mean (average) of the number of checks Jill wrote each month for the last four months. Add together the number of checks written each month: \(14 + 19 + 23 + 24 = 80\) checks. Since there are 4 months, divide the total by 4: \(80 ÷ 4 = 20\). Therefore, the mean number of checks Jill wrote each month is 20.

02

Estimate Monthly Per-check Fees

Multiply the mean number of checks by the fee per check to estimate the monthly per-check fees. The mean number of checks is 20 and the fee per check is $0.20. So, \(20 × $0.20 = $4.00\). Hence, Jill expects to pay approximately $4.00 in per-check fees each month.

03

Estimate Total Monthly Fees

Add the monthly per-check fees to the monthly maintenance fee to estimate the total monthly fees. The monthly per-check fees are $4.00 and the maintenance fee is $12.50, therefore: \( $4.00 + $12.50 = $16.50\). Jill will pay approximately $16.50 each month for the new checking account.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mean Number of Checks

When managing a checking account, it's essential to understand the pattern of your expenses, especially with frequent transactions like writing checks. The mean number of checks, simply put, is the average number you write over a period. To calculate this, you add the number of checks written each month and then divide by the number of months. In Jill's case, over four months, she wrote a total of 80 checks. Dividing this by 4, the mean number is 20 checks per month. Understanding this average is crucial because it allows you to predict future expenses related to your checking account.

For students trying to grasp this concept in financial algebra, remember that the mean gives you a sense of 'normal' activity for your account, which can help in budgeting and financial planning. It's the first step in managing your checking account fees effectively.

Per-Check Fees

Understanding Per-Check Fees

Per-check fees are charges that some banks impose each time a customer writes a check. These fees can add up over time and are an important aspect of the overall cost of a checking account. For example, with Jill's new account, she is charged \(0.20 for every check she writes. By multiplying the mean number of checks, 20 in Jill's case, by the per-check fee, Jill (and students alike) can estimate her monthly per-check expenses to be around \)4.00. Knowing how to calculate this is a practical application of financial algebra and helps with budgeting effectively.

Monthly Maintenance Fee

Apart from per-check fees, banks often charge a monthly maintenance fee for the services they provide. This fee is constant regardless of how many transactions are made during the month. For instance, Jill's account has a monthly maintenance fee of $12.50. This fee is a fixed expense and, hence, predictable when planning monthly finances. It's important for students to include this fee in their budget as it's a part of the total cost of owning a checking account, irrespective of the number of transactions.

Financial Algebra

Applying Financial Algebra to Real-life Problems

Financial algebra involves using mathematical concepts to solve real-world financial problems. It's a practical subject that brings algebra out of the abstract and into daily use. In Jill's situation, calculating the mean, assessing per-check fees, and adding the monthly maintenance fee to determine total account costs are all examples of financial algebra in action. It helps students develop financial literacy, preparing them for personal financial management. Such real-life applications demonstrate the relevance of algebra to everyday financial decisions.