K A = 8 Suppose that you drive 30,000 miles per year and gas averages $4 per gallon. Complete parts a. and b. below. a. What will you save in annual fuel expenses by owning a hybrid car averaging 30 miles per gallon rather than an SUV averaging 9 miles per gallon? $9332 (Round to the nearest dollar as needed.) b. If you deposit your monthly fuel savings at the end of each month into an annuity that pays 5.2% compounded monthly, how much will have saved at the end of nine years? (Round to the nearest dollar as needed.) 2

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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### Understanding Savings with a Hybrid Car and Investment Growth

#### Problem Context
Let's consider the following scenario: you drive 30,000 miles a year, and the average cost of gasoline is $4 per gallon. We'll explore the financial implications of switching from an SUV to a hybrid car and the potential growth of the savings from this switch if invested.

#### Given Formula
We will use the following formula to calculate the future value of a series of monthly deposits:

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

Where:
- \( A \) = the future value of the annuity
- \( P \) = the monthly deposit
- \( r \) = annual interest rate (as a decimal)
- \( n \) = number of times the interest is compounded per year
- \( t \) = number of years

#### Calculation Breakdown
We will calculate:
1. **Annual fuel savings by switching to a hybrid car.**
2. **The future value of the savings if invested at an interest rate of 5.2% compounded monthly for nine years.**

##### Part a: Annual Fuel Savings

**Given:**
- Hybrid car average miles per gallon: 30
- SUV average miles per gallon: 9
- Total miles driven per year: 30,000
- Cost of gas per gallon: $4

**Steps:**
1. Calculate the fuel consumption for both vehicles:
   - Hybrid car: \( \frac{30,000 \text{ miles}}{30 \text{ miles per gallon}} = 1,000 \text{ gallons} \)
   - SUV: \( \frac{30,000 \text{ miles}}{9 \text{ miles per gallon}} \approx 3,333.33 \text{ gallons} \)

2. Calculate the annual fuel cost for both vehicles:
   - Hybrid car: \( 1,000 \text{ gallons} \times $4 = $4,000 \)
   - SUV: \( 3,333.33 \text{ gallons} \times $4 \approx $13,333.33 \)

3. Calculate the annual savings:
   - Savings: \( $13,333.33 - $4,000 = $9,333.
Transcribed Image Text:### Understanding Savings with a Hybrid Car and Investment Growth #### Problem Context Let's consider the following scenario: you drive 30,000 miles a year, and the average cost of gasoline is $4 per gallon. We'll explore the financial implications of switching from an SUV to a hybrid car and the potential growth of the savings from this switch if invested. #### Given Formula We will use the following formula to calculate the future value of a series of monthly deposits: \[ A = P \left[ \left(1 + \frac{r}{n} \right)^{nt} - 1 \right] \div \left( \frac{r}{n} \right) \] Where: - \( A \) = the future value of the annuity - \( P \) = the monthly deposit - \( r \) = annual interest rate (as a decimal) - \( n \) = number of times the interest is compounded per year - \( t \) = number of years #### Calculation Breakdown We will calculate: 1. **Annual fuel savings by switching to a hybrid car.** 2. **The future value of the savings if invested at an interest rate of 5.2% compounded monthly for nine years.** ##### Part a: Annual Fuel Savings **Given:** - Hybrid car average miles per gallon: 30 - SUV average miles per gallon: 9 - Total miles driven per year: 30,000 - Cost of gas per gallon: $4 **Steps:** 1. Calculate the fuel consumption for both vehicles: - Hybrid car: \( \frac{30,000 \text{ miles}}{30 \text{ miles per gallon}} = 1,000 \text{ gallons} \) - SUV: \( \frac{30,000 \text{ miles}}{9 \text{ miles per gallon}} \approx 3,333.33 \text{ gallons} \) 2. Calculate the annual fuel cost for both vehicles: - Hybrid car: \( 1,000 \text{ gallons} \times $4 = $4,000 \) - SUV: \( 3,333.33 \text{ gallons} \times $4 \approx $13,333.33 \) 3. Calculate the annual savings: - Savings: \( $13,333.33 - $4,000 = $9,333.
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