You buy a house for $250,000. It is known to depreciate at 15% p.a. What will its value be 3 years after purchase?




To find the value of the house after 3 years given a depreciation rate of 15% per year, we can use the formula for exponential depreciation:

\[
V = P \times (1 - r)^t
\]

Where:
- $ V $ is the future value of the house.
- $ P $ is the initial value of the house ($250,000).
- $ r $ is the depreciation rate (15% or 0.15).
- $ t $ is the time in years (3 years).

Let's calculate this:

\[
V = 250,000 \times (1 - 0.15)^3
\]

Now solving this step by step.# Given values
P = 250000  # initial value of the house
r = 0.15    # depreciation rate
t = 3       # time in years

# Calculate the value of the house after 3 years
V = P * (1 - r) ** t
VThe value of the house after 3 years of depreciation at 15% per year will be approximately $153,531.25.

Would you like further details or explanations? 

Here are 8 related questions:
1. How would the value change after 5 years of depreciation?
2. What if the depreciation rate was only 10% instead of 15%?
3. How much value does the house lose each year?
4. Can you reverse depreciation to find the original value given the current value?
5. What if the house appreciated at 5% per year instead of depreciating?
6. How would monthly depreciation affect the value?
7. Can you compare depreciation with inflation effects on property value?
8. What happens if the depreciation rate changes annually?

**Tip:** Depreciation usually decreases value faster initially but slows down over time since the percentage is applied to a smaller amount each year.

Explore how to calculate the value of a house after 3 years with a 15% annual depreciation rate. Use our step-by-step solution to understand exponential depreciation and financial mathematics principles.

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