What is the second year's depreciation of a business which cost $53,300, if it depreciates at 12% p.a.?

To determine the second year's depreciation of a business that initially costs $53,300 and depreciates at 12% per annum, we need to follow these steps:

1. Calculate the value of the business after the first year.
2. Use this value to determine the depreciation for the second year.

### Step 1: Calculate the value after the first year

The formula for depreciation is:
\[ V = P (1 - r)^n \]

For the first year ($n = 1$):
\[ V_1 = 53,300 \times (1 - 0.12)^1 \]
\[ V_1 = 53,300 \times 0.88 \]
\[ V_1 = 46,904 \]

So, the value of the business after the first year is $46,904.

### Step 2: Calculate the depreciation for the second year

For the second year ($n = 1$ from the new value of $V_1$):
\[ V_2 = V_1 \times (1 - 0.12) \]
\[ V_2 = 46,904 \times 0.88 \]
\[ V_2 = 41,275.52 \]

So, the value of the business after the second year is $41,275.52.

To find the depreciation for the second year:
\[ \text{Second year's depreciation} = V_1 - V_2 \]
\[ \text{Second year's depreciation} = 46,904 - 41,275.52 \]
\[ \text{Second year's depreciation} = 5,628.48 \]

Thus, the second year's depreciation is $5,628.48.

Would you like any more details or have any questions?

Here are 8 related questions that expand on this information:
1. How would you calculate the total depreciation over 5 years?
2. What is the value of the business after 3 years with the same depreciation rate?
3. How would the depreciation amount change if the rate was 15% instead of 12%?
4. What is the cumulative depreciation after 4 years?
5. How do you account for salvage value in depreciation calculations?
6. How does straight-line depreciation differ from declining balance depreciation?
7. What would be the value after 2 years if the depreciation was compounded monthly?
8. How does the initial value of an asset affect the depreciation calculation?

**Tip:** When calculating depreciation over multiple years, it’s crucial to use the new depreciated value each year as the base for calculating the subsequent year’s depreciation.

Learn how to calculate the second year's depreciation for a business costing $53,300 with an annual depreciation rate of 12%. Follow step-by-step calculations using the depreciation formula. Suitable for high school students learning about financial mathematics and depreciation calculations.

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