How much value has been lost after 2 years on a ring originally costing $10,000 if it depreciates at 20% p.a.?

To find the value lost on a ring that depreciates at 20% per annum, originally costing $10,000, we can use the formula for depreciation. 

The value of the ring after $ n $ years can be calculated using the formula for exponential decay:
\[ V = P (1 - r)^n \]
where:
- $ V $ is the value after $ n $ years,
- $ P $ is the original value,
- $ r $ is the annual depreciation rate,
- $ n $ is the number of years.

Given:
- $ P = 10,000 $ dollars,
- $ r = 0.20 $ (since 20% is 0.20),
- $ n = 2 $ years.

First, we calculate the value of the ring after 2 years:
\[ V = 10,000 (1 - 0.20)^2 \]
\[ V = 10,000 (0.80)^2 \]
\[ V = 10,000 \times 0.64 \]
\[ V = 6,400 \] dollars.

The value of the ring after 2 years is $6,400. 

To find the value lost, we subtract this from the original value:
\[ \text{Value lost} = P - V \]
\[ \text{Value lost} = 10,000 - 6,400 \]
\[ \text{Value lost} = 3,600 \] dollars.

So, the value lost after 2 years is $3,600.

Would you like any more details or have any questions? 

Here are 8 related questions that expand on this information:
1. What would be the value of the ring after 3 years with the same depreciation rate?
2. How does the depreciation rate affect the value of an item over time?
3. Can you calculate the depreciation value if the rate changes to 25% p.a.?
4. How would the depreciation change if the rate was compounded monthly instead of annually?
5. What is the formula for calculating the future value of an item with continuous depreciation?
6. How much value would the ring retain after 5 years at a 20% annual depreciation rate?
7. If the ring's value depreciated linearly instead of exponentially, what would the value be after 2 years?
8. How would inflation affect the depreciation calculation if the rate of inflation is 3% per year?

**Tip:** When dealing with depreciation, always clarify whether the rate is applied annually, monthly, or continuously to ensure accurate calculations.

Learn how to calculate depreciation and the value lost on a ring originally costing $10,000 after 2 years. Understand the exponential decay formula and apply it to determine the decrease in value. Suitable for high school students learning about financial mathematics.

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