The value of a property depre clates every year by 10% of its value at the beginning of the year. The present value of the property is 8100. What was its value 2 years ago?

Options

A. 10000
B. `(90/100)^(2)xx8100`
C. `(100/110)^(2)xx8100`
D. 9801

Answer

To find the value of the property 2 years ago, we can follow these steps:

### Step 1: Understand the depreciation
The property depreciates by 10% each year. This means that at the end of each year, the property retains 90% of its value from the beginning of that year.

### Step 2: Calculate the effective value after 2 years
If the property retains 90% of its value each year, then after 2 years, the value can be calculated as:
\[ \text{Value after 2 years} = \text{Present Value} \times \left(0.9\right)^2 \]
Where \(0.9\) represents the 90% retained value.

### Step 3: Substitute the present value
Given that the present value of the property is 8100, we can substitute this into our equation:
\[ \text{Value after 2 years} = 8100 \times \left(0.9\right)^2 \]

### Step 4: Calculate \(0.9^2\)
Calculating \(0.9^2\):
\[ 0.9^2 = 0.81 \]

### Step 5: Calculate the value 2 years ago
Now substitute \(0.81\) back into the equation:
\[ \text{Value after 2 years} = 8100 \times 0.81 \]
Calculating this gives:
\[ \text{Value after 2 years} = 8100 \times 0.81 = 6561 \]

### Step 6: Find the original value 2 years ago
Since we want to find the original value 2 years ago, we can set up the equation:
\[ \text{Original Value} = \frac{\text{Present Value}}{0.81} \]
Substituting the present value:
\[ \text{Original Value} = \frac{8100}{0.81} \]

### Step 7: Calculate the original value
Calculating this gives:
\[ \text{Original Value} = 10000 \]

Thus, the value of the property 2 years ago was **10,000**.

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