Suppose that a certain car has the following average operating and ownership costs. 
Average Costs per Mile
Operating
Ownership
Total
$ 0.24
$ 0.72
​$0.96
a. If you drive 40 comma 000 miles per​ year, what is total annual expense for this​ car?
b. If the total annual expense for this car is deposited at the end of each year into an IRA paying 8.2​% compounded​ yearly, how much will be saved at the end of five ​years? Use the formula Upper A equals StartStartFraction Upper P left bracket left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript nt Baseline minus 1 right bracket OverOver left parenthesis StartFraction r Over n EndFraction right parenthesis EndEndFraction
.
Question content area bottom
Part 1
a. If you drive 40 comma 000 miles per​ year, the total annual expense for this car is ​$
  
enter your response here. 
​(Round to the nearest dollar as​ needed.)

To calculate the total annual expense for the car based on the average costs provided, follow these steps:

### Part a: Total Annual Expense

1. **Average Cost per Mile**:
   - Total average cost per mile = $0.96

2. **Miles Driven per Year**:
   - Annual miles = 40,000 miles

3. **Total Annual Expense Calculation**:
   \[
   \text{Total Annual Expense} = \text{Average Cost per Mile} \times \text{Miles Driven per Year}
   \]
   \[
   \text{Total Annual Expense} = 0.96 \times 40,000 = 38,400
   \]

Thus, the total annual expense for the car is **$38,400**.

### Part b: Future Value of Annual Deposits in IRA

Next, if you want to calculate how much will be saved at the end of five years by depositing this amount into an IRA that pays 8.2% compounded yearly, use the future value formula:

\[
A = \frac{P \left( (1 + \frac{r}{n})^{nt} - 1 \right)}{\frac{r}{n}}
\]

Where:
- $ P = 38,400 $ (annual deposit)
- $ r = 0.082 $ (annual interest rate)
- $ n = 1 $ (compounding frequency per year)
- $ t = 5 $ (years)

Plugging in the values:

1. Calculate $ A $:
   \[
   A = \frac{38400 \left( (1 + 0.082)^5 - 1 \right)}{0.082}
   \]

2. Calculate $ (1 + 0.082)^5 $:
   \[
   (1.082)^5 \approx 1.48024
   \]
   So,
   \[
   A = \frac{38400 \left( 1.48024 - 1 \right)}{0.082}
   \]
   \[
   A \approx \frac{38400 \times 0.48024}{0.082} \approx \frac{18495.88}{0.082} \approx 225,203.44
   \]

Thus, the amount saved at the end of five years will be approximately **$225,203**.

### Summary of Results:
- **Total Annual Expense**: $38,400
- **Amount Saved after 5 years**: $225,203

If you need any details or have further questions, let me know! Here are some related questions you might consider:

1. What factors influence the average cost per mile for a vehicle?
2. How can varying the interest rate affect savings over time?
3. What are the benefits of using an IRA for retirement savings?
4. How do ownership costs differ between various types of vehicles?
5. What strategies can be used to reduce operating costs for a car?

**Tip**: Regularly review your expenses to identify areas where you can save on ownership costs, such as maintenance or insurance.

Suppose that a certain car has the following average operating and ownership costs. Average Costs per Mile Operating $0.24 Ownership $0.72 Total $0.96 a. If you drive 40,000 miles per year, what is the total annual expense for this car? b. If the total annual expense for this car is deposited at the end of each year into an IRA paying 8.2% compounded yearly, how much will be saved at the end of five years?

Discover how to calculate the total annual expense for a car based on average operating and ownership costs and determine future savings from annual deposits into an IRA at 8.2% interest over five years. Total annual expense calculated as $38,400, with future savings approximately $225,203.

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