Mark has a debt to Adele and is making regular payments from his bank account. We need to determine the approximate balance remaining in his account after 16 months, given that he withdraws 11% of the account balance each month and started with $9050.4000. This problem involves calculating the depreciation of the accou...
The Depreciation Formula
The formula for depreciation, which calculates the value of something that decreases over time, is:
y = A(1 - r)^t
Where:
- y = the final value after time t
- A = the initial amount (principal)
- r = the depreciation rate (in this case, the withdrawal rate)
- t = the time period (in months)
Applying the Formula
In this case, we have:
- A = $9050.4000
- r = 11% = 0.11
- t = 16 months
Substituting these values into the formula, we get:
y = $9050.4000(1 - 0.11)^16
Calculating this expression gives us:
y ≈ $2026.92
The Approximate Balance
Therefore, the approximate balance in Mark's bank account after 16 months would be approximately $2026.92. This illustrates how the repeated withdrawal of a percentage of the account balance leads to a significant decrease in the total amount over time. This method is often used to calculate the value of assets that depreciate, such as vehicles or machinery, over their lifespan.
Understanding Depreciation
Depreciation is a common concept used to understand the decline in value of assets over time. This decline can be caused by a number of factors, including wear and tear, obsolescence, or simply the passage of time. The depreciation formula helps to quantify this decline and can be used in various financial applications, such as:
- Accounting: Depreciation is used to calculate the value of assets for financial reporting purposes.
- Taxation: Depreciation can be used to deduct the cost of assets from taxable income over time.
- Financial Planning: Depreciation can be used to estimate the future value of assets and plan for their replacement.
Key Points to Remember
- The depreciation formula can be used to calculate the value of any asset that depreciates over time.
- The depreciation rate is the percentage of the asset's value that is lost each year.
- The depreciation formula is a powerful tool for financial planning and decision-making.
Conclusion
By applying the depreciation formula, we have calculated that the approximate balance in Mark's bank account after 16 months would be $2026.92. This example demonstrates the practical application of this formula in calculating the value of an asset that depreciates over time. Understanding depreciation is essential for anyone dealing with financial matters, as it allows us to make informed decisions about the value of assets and plan for their future.