Select The Correct Answer From Each Drop-down Menu.The Function F ( X ) = 2 , 000 ( 1 + 0.0225 12 ) 12 T F(x)=2,000\left(1+\frac{0.0225}{12}\right)^{12t} F ( X ) = 2 , 000 ( 1 + 12 0.0225 ​ ) 12 T Models The Balance In A Savings Account.The Savings Account Had An Initial Balance Of □ \square □ And Compounds

The given function $f(x)=2,000\left(1+\frac{0.0225}{12}\right)^{12t}$ represents the balance in a savings account. To understand this model, we need to break down the components and analyze each part.

Initial Balance

The initial balance of the savings account can be found by evaluating the function at $t=0$. This is because the initial balance is the balance at the beginning, when the time $t$ is zero.

f(0) = 2,000\left(1+\frac{0.0225}{12}\right)^{12(0)}

Simplifying the expression, we get:

f(0) = 2,000\left(1+\frac{0.0225}{12}\right)^{0}

Since any number raised to the power of zero is equal to 1, we have:

f(0) = 2,000(1)

Therefore, the initial balance of the savings account is $2,000.

Compounding Frequency

The compounding frequency is the number of times the interest is compounded per year. In this case, the interest is compounded monthly, as indicated by the fraction $\frac{0.0225}{12}$.

Monthly Interest Rate

The monthly interest rate is the interest rate divided by the number of compounding periods per year. In this case, the monthly interest rate is:

\frac{0.0225}{12} = 0.001875

Growth Rate

The growth rate is the rate at which the balance grows over time. In this case, the growth rate is:

\left(1+\frac{0.0225}{12}\right)^{12t}

This represents the growth factor, which is applied to the initial balance to get the balance at any given time $t$.

Savings Account Balance

The balance in the savings account at any given time $t$ can be found by evaluating the function $f(x)=2,000\left(1+\frac{0.0225}{12}\right)^{12t}$.

f(t) = 2,000\left(1+\frac{0.0225}{12}\right)^{12t}

This represents the balance in the savings account at time $t$, taking into account the initial balance, compounding frequency, and growth rate.

Selecting the Correct Answer

Based on the analysis above, we can conclude that the savings account had an initial balance of $2,000 and compounds monthly with a monthly interest rate of 0.001875.

Conclusion

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Q: What is the purpose of the savings account model?

A: The savings account model is used to calculate the balance in a savings account over time, taking into account the initial balance, compounding frequency, and growth rate.

Q: What is the initial balance of the savings account?

A: The initial balance of the savings account is $2,000.

Q: How often is the interest compounded in the savings account?

A: The interest is compounded monthly in the savings account.

Q: What is the monthly interest rate in the savings account?

A: The monthly interest rate in the savings account is 0.001875.

Q: How does the growth rate affect the balance in the savings account?

A: The growth rate affects the balance in the savings account by applying a growth factor to the initial balance. The growth factor is calculated as:

\left(1+\frac{0.0225}{12}\right)^{12t}

This represents the growth factor, which is applied to the initial balance to get the balance at any given time $t$.

Q: How can I use the savings account model to calculate the balance at a specific time?

A: To calculate the balance at a specific time, you can evaluate the function $f(x)=2,000\left(1+\frac{0.0225}{12}\right)^{12t}$ at the desired time $t$. For example, to calculate the balance at time $t=5$, you would evaluate:

f(5) = 2,000\left(1+\frac{0.0225}{12}\right)^{12(5)}

Q: What are some real-world applications of the savings account model?

A: The savings account model has many real-world applications, including:

• Calculating the balance in a savings account over time
• Determining the interest rate needed to reach a specific balance
• Comparing the performance of different savings accounts
• Planning for long-term financial goals, such as retirement or a down payment on a house

Q: Can I use the savings account model to calculate the balance in a different type of account?

A: While the savings account model is specifically designed for calculating the balance in a savings account, you can modify the model to suit other types of accounts. For example, you could use a different interest rate or compounding frequency to calculate the balance in a certificate of deposit (CD) or a high-yield savings account.

Q: Are there any limitations to the savings account model?

A: Yes, there are several limitations to the savings account model. These include:

• The model assumes a fixed interest rate and compounding frequency, which may not reflect real-world conditions
• The model does not take into account fees or other charges that may be associated with the account
• The model is based on a simplified formula and may not accurately reflect the actual balance in the account

Conclusion

In conclusion, the savings account model is a powerful tool for calculating the balance in a savings account over time. By understanding the components of the model and how they interact, you can use the model to make informed decisions about your finances and achieve your long-term goals.