the car depreciates at a rate of 18% per annum. how much will it be worth when you have finished paying off your loan in 5 years time? (car with loan interest costs $36436.50)

To calculate the future value of the car after 5 years, given that it depreciates at a rate of 18% per annum, we can use the formula for exponential decay:

\[
\text{Future Value} = \text{Present Value} \times (1 - \text{Depreciation Rate})^{\text{Number of Years}}
\]

Here:
- **Present Value** = $36,436.50
- **Depreciation Rate** = 18% per annum (or 0.18 in decimal form)
- **Number of Years** = 5

Now let's calculate:

\[
\text{Future Value} = 36,436.50 \times (1 - 0.18)^5
\]

\[
\text{Future Value} = 36,436.50 \times (0.82)^5
\]

\[
\text{Future Value} \approx 36,436.50 \times 0.418211328
\]

\[
\text{Future Value} \approx 15,239.68
\]

So, after 5 years, the car will be worth approximately **$15,239.68**.

Would you like further details or have any other questions? 

Here are 5 related questions:
1. How would the car's value change if the depreciation rate was different?
2. What if the loan period was extended to 7 years instead of 5?
3. How would you calculate the total depreciation over the 5 years?
4. Can this method be applied to other types of assets? How?
5. How would you adjust the calculation if the depreciation rate varied each year?

**Tip:** When dealing with exponential decay, the base value (in this case, $1 - \text{Depreciation Rate}$) is raised to the power of the time period to reflect the compounding effect over time.

Learn how to calculate the future value of a car that depreciates at 18% per annum over 5 years. Use our step-by-step formula for exponential decay with a present value of $36,436.50. Explore scenarios like changing depreciation rates and loan periods. Ideal for finance and math enthusiasts.

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