Your car is years old and is worth $8500 now and will drop in value by 19% per year thereafter. O&M costs are $3800 this year and will rise by 6% per year thereafter. Assume i = 10%. Calculate the Total EAC if you keep the car for 2 years.
DO NOT ENTER AS A NEGATIVE NUMBER.
Round your final answer to the nearest whole number (integer). Round interim calculations to 4 decimal points. Do not include any dollar signs, percentage % signs, commas, decimal places and/or spaces in your answer. Your answer should only include numbers.
For example, if the correct answer is 1021, you should enter 1021 as your answer. If you enter $1021 or 1,021 or $1,021 or 1 021 or $1021.00, your answer will be marked wrong.
Answer:

To solve for the Total Equivalent Annual Cost (EAC) if you keep the car for 2 years, we need to consider both the depreciation in value of the car and the operation & maintenance (O&M) costs over these 2 years.

### Steps:

1. **Depreciation of the Car's Value:**
   - Current value = $8500
   - Depreciation rate = 19% per year

   Calculate the value at the end of Year 1 and Year 2:
   \[
   \text{Value at end of Year 1} = 8500 \times (1 - 0.19) = 8500 \times 0.81
   \]
   \[
   \text{Value at end of Year 2} = 8500 \times (0.81)^2
   \]

2. **O&M Costs:**
   - O&M cost for Year 1 = $3800
   - O&M cost increases by 6% each year

   Calculate the O&M costs for Year 1 and Year 2:
   \[
   \text{O&M for Year 1} = 3800
   \]
   \[
   \text{O&M for Year 2} = 3800 \times (1 + 0.06)
   \]

3. **Present Value of Costs:**
   Use the discount rate $ i = 10\% $ to find the present value (PV) of these costs.
   \[
   \text{PV of O&M costs for Year 1} = \frac{\text{O&M for Year 1}}{(1 + i)^1}
   \]
   \[
   \text{PV of O&M costs for Year 2} = \frac{\text{O&M for Year 2}}{(1 + i)^2}
   \]

4. **Equivalent Annual Cost (EAC):**
   The EAC is the uniform annual cost that equates to the PV of all costs.
   \[
   \text{Total PV} = \text{PV of O&M for Year 1} + \text{PV of O&M for Year 2}
   \]
   The EAC can be calculated using:
   \[
   \text{EAC} = \frac{\text{Total PV}}{\text{Present Value Annuity Factor (PVAF)}}
   \]
   where PVAF for 2 years and $ i = 10\% $ is:
   \[
   \text{PVAF} = \frac{1 - (1 + i)^{-2}}{i}
   \]

Let's calculate this.The Total Equivalent Annual Cost (EAC) if you keep the car for 2 years is **3909**.

Do you have any questions or would you like details on the calculations?

Here are 8 related questions you might find interesting:

1. How would the EAC change if the depreciation rate was 15% instead of 19%?
2. What would be the effect on EAC if the O&M costs increase by 8% per year instead of 6%?
3. How would the EAC be different if the discount rate were 8% instead of 10%?
4. What is the EAC if you plan to keep the car for 3 years?
5. How does the initial value of the car affect the Total EAC?
6. What if the O&M costs start at $4500 instead of $3800? How would the EAC change?
7. How does the calculation of EAC vary between 1-year and 2-year periods?
8. If you sell the car after 2 years, how would that impact the EAC calculation?

**Tip:** When working with EAC calculations, remember that the discount rate significantly influences the final value, so it's essential to choose it accurately based on the scenario.

Learn how to calculate the Total Equivalent Annual Cost (EAC) for a car over 2 years using financial mathematics. This problem involves depreciation calculations, operation & maintenance cost projections, and discounting future cash flows. Round your final answer to the nearest whole number.

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