Problem 71 - Beginning and Intermediate Algebra

Question

This month Warren deposited \(\$ 1500\) into a bank account. He will deposit \(\$ 100\) into the account at the beginning of each month. Disregarding interest, how much money will Warren have saved after 9 months?

Step-by-Step Solution

Answer

Warren will have a total of $2400 saved in the bank account after 9 months, disregarding interest.

Step 1: Find the total amount Warren will deposit in the next 9 months.

Since Warren will deposit $100 each month for 9 months, we can find the total amount of these deposits by multiplying the monthly deposit amount by the number of months: \(100 \times 9\).

Step 2: Calculate the total deposited amount.

Multiply the monthly deposit by the number of months to find the total amount Warren will deposit over the 9 months: \[100 \times 9 = 900\]

Step 3: Add the initial deposit to the total deposited amount.

Warren started with a deposit of \(1500 and deposited an additional \)900 over the next 9 months. To find the total amount he saved after 9 months, add these two amounts together: \[1500 + 900\]

Step 4: Compute the total amount saved.

Add the initial deposit and the total amount deposited over the next 9 months: \[1500 + 900 = 2400\] Warren will have a total of $2400 saved in the bank account after 9 months, disregarding interest.

Key Concepts

Deposits and Savings

Learning how deposits and savings work can help you manage your money better. If you put money into a bank account, such as Warren's initial deposit of $1500, it can grow over time. Adding regular deposits increases your savings.
Warren's example shows how to consistently save money. By depositing $100 each month, he's using a strategy to increase his savings systematically. This is a basic savings plan, where you start with a lump sum—like $1500 here—and then add to it regularly.
The benefit of this approach is that every little deposit counts.

• Begin with a lump sum to "jump-start" your savings.
• Make regular monthly deposits to steadily increase your savings.
• Keep track of your total savings to motivate you.

Understanding this simple method can be the first step in managing your personal savings effectively.

Basic Algebra

Basic Algebra is a powerful tool in calculating and predicting outcomes. It consists of working with numbers and variables to solve equations. In Warren's savings plan, we use basic algebra to find how much he will save over 9 months.
The key steps were straight multiplication and addition. First, multiply the consistent deposit amount each month (\(100) by the number of months (9). So, we have: \[100 \times 9 = 900\]
This tells us that Warren deposits an additional \)900 over the period.
Then, add this to the initial deposit:\[1500 + 900 = 2400\]
This shows the final amount saved. Algebra simplifies calculating this increase from both the regular deposits and the initial one.

• Use multiplication to find total regular deposits over a period.
• Addition combines the initial amount with these regular deposits.

Basic Algebra is all about breaking down a problem into manageable parts, which makes managing finances easier.

Time and Money Management

Managing your time and money effectively can significantly affect your savings. In Warren's case, he's using a well-planned savings schedule to ensure he has enough over nine months.
Time management in savings signifies setting aside specific amounts regularly to build your financial security. Money management involves understanding what you need to save each month to reach a desired total.
The importance of this is seen in following a schedule:

• Plan your deposits ahead for a clear financial map.
• Stay consistent with your deposits to achieve your savings goal.

Here, Warren's steady monthly deposit illustrates commitment to a plan. This consistent schedule leads him to achieve $2400 in the bank. Effective time and money management shows that even small, regular contributions lead to significant savings over time.