A Long-running Asset Account Has A Balance That Has Doubled Each Year Over The Last 10 Years. At What Point Was The Balance Half Its Current Balance?A. Year 1 B. Year 5 C. Year 7 D. Year 9

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A Long-Running Asset Account: Unraveling the Mystery of Doubling Balances

In the world of finance and accounting, asset accounts play a crucial role in tracking the value of a company's assets over time. One common phenomenon observed in asset accounts is the doubling of balances, which can be attributed to various factors such as investments, sales, or other business activities. In this article, we will delve into a specific scenario where a long-running asset account has doubled in balance each year over the last 10 years. Our objective is to determine at what point the balance was half its current balance.

Understanding the Concept of Doubling Balances

Before we dive into the problem, let's understand the concept of doubling balances. When an asset account doubles in balance each year, it means that the balance at the end of each year is twice the balance at the end of the previous year. This can be represented mathematically as:

Balance at the end of Year 1 = 2 × Balance at the end of Year 0 Balance at the end of Year 2 = 2 × Balance at the end of Year 1 Balance at the end of Year 3 = 2 × Balance at the end of Year 2 ... Balance at the end of Year 10 = 2 × Balance at the end of Year 9

Let's assume that the balance of the asset account has doubled each year over the last 10 years. We want to find out at what point the balance was half its current balance. To do this, we need to work backwards from the current balance.

Working Backwards

Let's denote the current balance as B. Since the balance doubles each year, we can represent the balance at the end of each year as follows:

Balance at the end of Year 10 = 2 × Balance at the end of Year 9 Balance at the end of Year 9 = 2 × Balance at the end of Year 8 Balance at the end of Year 8 = 2 × Balance at the end of Year 7 ... Balance at the end of Year 1 = 2 × Balance at the end of Year 0

We want to find the point at which the balance was half its current balance. Let's denote this point as Year X. At this point, the balance was half its current balance, which means that the balance at the end of Year X was B/2.

Solving for Year X

Since the balance doubles each year, we can represent the balance at the end of each year as follows:

Balance at the end of Year X = 2 × Balance at the end of Year X-1 Balance at the end of Year X-1 = 2 × Balance at the end of Year X-2 ... Balance at the end of Year 1 = 2 × Balance at the end of Year 0

We know that the balance at the end of Year X was B/2. Therefore, we can write:

Balance at the end of Year X = 2 × Balance at the end of Year X-1 B/2 = 2 × Balance at the end of Year X-1

Simplifying the equation, we get:

Balance at the end of Year X-1 = B/4

Since the balance doubles each year, we can continue working backwards:

Balance at the end of Year X-2 = B/8 Balance at the end of Year X-3 = B/16 ... Balance at the end of Year 0 = B/2^X

We want to find the value of X. Since the balance at the end of Year 0 is B/2^X, we can set up the following equation:

B/2^X = B/2

Simplifying the equation, we get:

2^X = 2

Taking the logarithm base 2 of both sides, we get:

X = 1

Therefore, the balance was half its current balance at the end of Year 1. This means that the correct answer is A. Year 1.

The final answer is A. Year 1.
A Long-Running Asset Account: Unraveling the Mystery of Doubling Balances

In our previous article, we explored the concept of doubling balances in asset accounts and solved a problem to determine at what point the balance was half its current balance. In this article, we will answer some frequently asked questions related to doubling balances and asset accounts.

Q: What is a doubling balance in an asset account?

A: A doubling balance in an asset account refers to a situation where the balance of the account doubles each year. This can be attributed to various factors such as investments, sales, or other business activities.

Q: How do I calculate the doubling balance of an asset account?

A: To calculate the doubling balance of an asset account, you can use the following formula:

Balance at the end of Year 1 = 2 × Balance at the end of Year 0 Balance at the end of Year 2 = 2 × Balance at the end of Year 1 Balance at the end of Year 3 = 2 × Balance at the end of Year 2 ... Balance at the end of Year 10 = 2 × Balance at the end of Year 9

Q: What is the formula for working backwards to find the point at which the balance was half its current balance?

A: To work backwards and find the point at which the balance was half its current balance, you can use the following formula:

Balance at the end of Year X = 2 × Balance at the end of Year X-1 Balance at the end of Year X-1 = 2 × Balance at the end of Year X-2 ... Balance at the end of Year 1 = 2 × Balance at the end of Year 0

Q: How do I determine the value of X in the formula?

A: To determine the value of X, you can set up the following equation:

B/2^X = B/2

Simplifying the equation, you get:

2^X = 2

Taking the logarithm base 2 of both sides, you get:

X = 1

Q: What is the significance of the point at which the balance was half its current balance?

A: The point at which the balance was half its current balance is significant because it represents the point at which the balance was equal to half of its current value. This can be useful in various financial and accounting applications.

Q: Can I apply the concept of doubling balances to other types of accounts?

A: Yes, the concept of doubling balances can be applied to other types of accounts, such as liability accounts or equity accounts. However, the formula and calculations may vary depending on the type of account and the specific scenario.

Q: What are some common applications of doubling balances in finance and accounting?

A: Doubling balances have various applications in finance and accounting, including:

  • Investment analysis: Doubling balances can be used to analyze the growth of investments over time.
  • Financial planning: Doubling balances can be used to plan for future financial needs and goals.
  • Accounting: Doubling balances can be used to track the growth of asset accounts over time.

In conclusion, doubling balances are a common phenomenon in asset accounts, and understanding the concept and formula can be useful in various financial and accounting applications. We hope that this Q&A article has provided you with a better understanding of doubling balances and asset accounts.