Problem 58 - Elementary Algebra

Question

A student overdraws a bank account about five times each month. Predict the total overdraft fees the student will pay in 1 year. Chase's overdraft fees are \(\$ 25\) for the first fee each year, \(\$ 32\) for the next four and \(\$ 35\) after that. (Source: www.nytimes .com, Sept. 23, 2009)

Step-by-Step Solution

Answer

The total overdraft fees for the year are \(\$2078\).

Step 1 - Calculate the number of overdrafts per year

To find out how many times the student will overdraw in a year, multiply the monthly overdrafts by the number of months in a year. Since the student overdrafts 5 times each month, then in a year: \(5 \times 12 = 60\) overdrafts.

Step 2 - Determine the fee structure for the first overdraft

The first overdraft of the year costs \(\$25\).

Step 3 - Calculate the fees for the next four overdrafts

The next four overdrafts cost \(\$32\) each. Therefore, the total cost for these four overdrafts is: \(4 \times 32 = 128\).

Step 4 - Calculate the fees for the remaining overdrafts

Subtract the first 5 overdrafts from the total to find the number of remaining overdrafts: \(60 - 5 = 55\). Each remaining overdraft costs \(\$35\), so the total cost for these overdrafts is: \(55 \times 35 = 1925\).

Step 5 - Add up all fees

Add the fees together to find the total amount paid in overdraft fees: \(25 + 128 + 1925 = 2078\).

Key Concepts

Bank Overdraft Calculations

When you spend more money than what you have in your bank account, this is called an overdraft. Some banks charge fees for overdrafts. In our problem, Chase's overdraft fees include different charges depending on the number of overdrafts. Here’s how you can calculate these fees:

• Check how many times the overdraft occurs monthly.
• Calculate the overdrafts annually by multiplying monthly overdrafts by 12.
• Apply different fees for the first, next, and remaining overdrafts as given in the problem’s fee structure.

Understanding how to calculate these fees helps in managing personal finances better and avoiding unexpected charges. Keeping track of overdrafts can save money in the long run.

Annual Financial Predictions

Annual financial predictions allow you to estimate future financial outcomes based on current or past data. In our example, the student overdraws 5 times a month. To find out the annual number of overdrafts, you multiply this by the 12 months in a year.
This gives us:
\[5 \times 12 = 60 \] overdrafts per year.
Predicting these figures helps in planning better financially. If you know the fixed and variable fees, you can compute the total annual expense.
Having an idea about the future expenses can help in budgeting and setting financial goals more effectively. It also allows to adjust spending habits and find ways to minimize unnecessary costs like bank fees.

Multiplication and Subtraction in Problem Solving

To solve problems involving multiple steps and varying conditions, use basic operations like multiplication and subtraction. In our overdraft fee calculation example, we used these operations as follows:

• First, we multiplied the number of monthly overdrafts by 12 to find the annual figure.
• Then, we calculated fees by multiplying quantities and fees together, such as \[4 \times 32 \] for the next four overdrafts.
• Finally, we subtracted the first 5 overdrafts from the total number and calculated fees for the remaining ones.

This process involves breaking down a problem into smaller, manageable steps. Each step utilizes basic arithmetic operations to move towards finding the ultimate solution. Understanding these principles can help solve many real-world problems efficiently.