Franklin Deposited $ 75 \$75 $75 In A No-interest Bank Account When He Opened It. After That, He Deposits $ 50 \$50 $50 Per Month In The Account. Assume He Makes No Other Withdrawals Or Deposits. The Equation Below Can Be Used To Find M M M ,

Mar 11, 2025 by ADMIN 243 views

Understanding Franklin's Bank Account

Franklin deposited $\$75$ in a no-interest bank account when he opened it. After that, he deposits $\$50$ per month in the account. Assume he makes no other withdrawals or deposits. The equation below can be used to find $m$ , the number of months Franklin has had the account.

The equation to find $m$ is given by:

75 + 50m = A

where $A$ is the total amount in the account after $m$ months.

Let's break down the equation to understand it better. The left-hand side of the equation consists of two terms:

Initial Deposit: $75$ is the initial deposit made by Franklin when he opened the account.
Monthly Deposits: $50m$ represents the total amount deposited by Franklin over $m$ months. Since he deposits $\$50$ per month, the total amount deposited is $50 \times m$ .

The right-hand side of the equation is the total amount in the account after $m$ months, denoted by $A$ .

To find the number of months Franklin has had the account, we need to solve for $m$ . We can do this by isolating $m$ on one side of the equation.

First, let's subtract $75$ from both sides of the equation:

50m = A - 75

Next, let's divide both sides of the equation by $50$ :

m = \frac{A - 75}{50}

The equation $m = \frac{A - 75}{50}$ gives us the number of months Franklin has had the account. To find the value of $m$ , we need to know the total amount in the account after $m$ months, denoted by $A$ .

For example, if the total amount in the account after $m$ months is $\$2000$ , we can plug this value into the equation to find the value of $m$ :

m = \frac{2000 - 75}{50}

m = \frac{1925}{50}

m = 38.5

Therefore, Franklin has had the account for approximately $38.5$ months.

In conclusion, the equation $75 + 50m = A$ can be used to find the number of months Franklin has had the account. By breaking down the equation and solving for $m$ , we can find the value of $m$ given the total amount in the account after $m$ months.

The equation $75 + 50m = A$ has several real-world applications. For example, it can be used to calculate the number of months a person has had a savings account, a credit card, or a loan. It can also be used to calculate the number of months a business has had a bank account or a loan.

Here are some example use cases for the equation $75 + 50m = A$ :

A person deposits $\$100$ per month in a savings account and has a total balance of $\$3000$ . How many months has the person had the account?
A business deposits $\$500$ per month in a bank account and has a total balance of $\$15,000$ . How many months has the business had the account?
A person has a credit card with a balance of $\$2000$ and makes a monthly payment of $\$100$ . How many months has the person had the credit card?

To solve for $m$ in real-world scenarios, we need to know the total amount in the account after $m$ months, denoted by $A$ . We can then plug this value into the equation $m = \frac{A - 75}{50}$ to find the value of $m$ .

For example, if the total amount in the account after $m$ months is $\$2000$ , we can plug this value into the equation to find the value of $m$ :

m = \frac{2000 - 75}{50}

m = \frac{1925}{50}

m = 38.5

Therefore, the person has had the account for approximately $38.5$ months.

In conclusion, the equation $75 + 50m = A$ can be used to find the number of months a person or business has had a bank account, credit card, or loan. By breaking down the equation and solving for $m$ , we can find the value of $m$ given the total amount in the account after $m$ months.

The equation $75 + 50m = A$ is a simple yet powerful tool for calculating the number of months a person or business has had a bank account, credit card, or loan. By understanding the equation and how to solve for $m$ , we can make informed decisions about our finances and achieve our financial goals.

[1] "Algebra and Trigonometry" by Michael Sullivan
[2] "Mathematics for the Nonmathematician" by Morris Kline
[3] "Financial Mathematics" by Robert M. Anderson

Initial Deposit: The amount deposited by a person or business when they open a bank account or take out a loan.
Monthly Deposits: The amount deposited by a person or business each month.
Total Amount: The total amount in the account after $m$ months.
Number of Months: The number of months a person or business has had a bank account, credit card, or loan.
Franklin's Bank Account: Q&A

In our previous article, we discussed Franklin's bank account and the equation $75 + 50m = A$ that can be used to find the number of months Franklin has had the account. In this article, we will answer some frequently asked questions about Franklin's bank account and the equation.

A: The initial deposit in Franklin's bank account is $\$75$ . This is the amount deposited by Franklin when he opened the account.

A: Franklin deposits $\$50$ per month in his bank account.

A: The total amount in Franklin's bank account after $m$ months is denoted by $A$ . This is the amount in the account after $m$ months of deposits.

A: To use the equation $75 + 50m = A$ to find the number of months Franklin has had the account, you need to know the total amount in the account after $m$ months, denoted by $A$ . You can then plug this value into the equation to find the value of $m$ .

A: The formula for finding the number of months Franklin has had the account is:

m = \frac{A - 75}{50}

A: To use the formula to find the number of months Franklin has had the account, you need to know the total amount in the account after $m$ months, denoted by $A$ . You can then plug this value into the formula to find the value of $m$ .

A: If you don't know the total amount in the account after $m$ months, you can't use the equation or formula to find the number of months Franklin has had the account. However, you can use other methods to estimate the number of months, such as using a financial calculator or consulting with a financial advisor.

A: The equation and formula can be used to find the number of months for any type of account that has a fixed monthly deposit and no interest. However, if the account has interest or other fees, the equation and formula may not be accurate.

A: Yes, there are other ways to find the number of months for an account, such as using a financial calculator or consulting with a financial advisor. You can also use online tools or software to calculate the number of months.

In conclusion, the equation $75 + 50m = A$ and the formula $m = \frac{A - 75}{50}$ can be used to find the number of months Franklin has had the account. By understanding the equation and formula, you can make informed decisions about your finances and achieve your financial goals.

[1] "Algebra and Trigonometry" by Michael Sullivan
[2] "Mathematics for the Nonmathematician" by Morris Kline
[3] "Financial Mathematics" by Robert M. Anderson

Initial Deposit: The amount deposited by a person or business when they open a bank account or take out a loan.
Monthly Deposits: The amount deposited by a person or business each month.
Total Amount: The total amount in the account after $m$ months.
Number of Months: The number of months a person or business has had a bank account, credit card, or loan.