Use the following formula. nt P 1+ 47* A = C Suppose that you drive 50,000 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 50 miles per gallon rather than an SUV averaging 25 miles per gallon? $ (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 4.8% compounded monthly, how much will have saved at the end of seven years? $ (Round to the nearest dollar as needed.)

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
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1.11: Answer A and B questions
Sure! Here's the transcription and explanation of the content from the image:

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### Use the following formula:
\[ 
A = P \left( \frac{\left(1 + \frac{r}{n}\right)^{nt} - 1}{\frac{r}{n}} \right) 
\]

**Suppose that you drive 50,000 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 50 miles per gallon rather than an SUV averaging 25 miles per gallon?

$[ \_\_\_\_ ]

(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 4.8% compounded monthly, how much will you have saved at the end of seven years?

$[ \_\_\_\_ ]

(Round to the nearest dollar as needed.)

---

### Explanation:

The formula provided is the future value of an ordinary annuity, where:
- \( A \) is the future value of the annuity.
- \( P \) is the periodic payment (monthly savings in this context).
- \( r \) is the annual interest rate (4.8% in this case).
- \( n \) is the number of compounding periods per year (12 for monthly).
- \( t \) is the number of years the money is invested (7 years here).

In part a, you calculate the difference in annual fuel costs between a hybrid car and an SUV. In part b, you invest the savings monthly into an annuity to find the future value after seven years.
Transcribed Image Text:Sure! Here's the transcription and explanation of the content from the image: --- ### Use the following formula: \[ A = P \left( \frac{\left(1 + \frac{r}{n}\right)^{nt} - 1}{\frac{r}{n}} \right) \] **Suppose that you drive 50,000 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 50 miles per gallon rather than an SUV averaging 25 miles per gallon? $[ \_\_\_\_ ] (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 4.8% compounded monthly, how much will you have saved at the end of seven years? $[ \_\_\_\_ ] (Round to the nearest dollar as needed.) --- ### Explanation: The formula provided is the future value of an ordinary annuity, where: - \( A \) is the future value of the annuity. - \( P \) is the periodic payment (monthly savings in this context). - \( r \) is the annual interest rate (4.8% in this case). - \( n \) is the number of compounding periods per year (12 for monthly). - \( t \) is the number of years the money is invested (7 years here). In part a, you calculate the difference in annual fuel costs between a hybrid car and an SUV. In part b, you invest the savings monthly into an annuity to find the future value after seven years.
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