Question

It depreciates at a rate of 11% a year. Interest is compounded yearly. What is the value after 9 years? Round your answer to the nearest penny.

Answer 1

After 9 years, the value will be approximately $418.76.

Step-by-step explanation:

Depreciation and compounding interest can significantly impact the value of an asset over time. In this scenario, with a depreciation rate of 11% per year and compounded yearly, the formula for calculating the future value (FV) can be expressed as:

`\[ FV = PV * (1 - \text{{depreciation rate}})^{\text{{number of years}}} \]`

Where:

`- \( FV \)` is the future value,

`- \( PV \)` is the present value,

- The depreciation rate is 11% (or 0.11), and

- The number of years is 9.

Substituting these values into the formula:

`\[ FV = PV * (1 - 0.11)^9 \]`

This calculation yields the future value of the asset after 9 years. The compounding effect of depreciation over each year results in a reduced value. Rounding to the nearest penny gives us the final answer of $418.76.

Understanding the mechanics of this formula reveals that the asset loses 11% of its value each year, and this cumulative effect compounds annually. Hence, the decreasing value accelerates as time progresses. This result is crucial for financial planning and assessing the long-term impact of depreciation on the asset's value.