Question

8.6.7 owning & operating cars
name

1. using the table above determine the following.

a. if you drive 14,000 miles per year, what is the total annual expense for an electric vehicle?

b. if the total annual expense for an electric vehicle 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 six years?

1. if you drive 30,000 miles per year, by how much does the total annual expense for a large sedan exceed that of an electric vehicle over six years?

Explanation:

Step1: Calculate annual expense for electric vehicle (part a)

The total cost per mile for an electric vehicle is $0.61$. If you drive $14000$ miles per year, the annual expense $E$ is calculated by multiplying the cost per mile by the number of miles.
$$E = 14000\times0.61$$
$$E=8540$$

Step2: Use the future - value of an ordinary annuity formula (part b)

The formula for the future - value of an ordinary annuity is $F = A\times\frac{(1 + r)^{n}-1}{r}$, where $A$ is the annual payment, $r$ is the interest rate per period, and $n$ is the number of periods.
Here, $A = 8540$, $r=0.082$, and $n = 6$.
First, calculate $(1 + r)^{n}=(1 + 0.082)^{6}\approx1.082^{6}\approx1.537977$.
Then, $(1 + r)^{n}-1\approx1.537977- 1=0.537977$.
Next, $\frac{(1 + r)^{n}-1}{r}=\frac{0.537977}{0.082}\approx6.5607$.
Finally, $F=8540\times6.5607\approx56028.38$

Step3: Calculate annual expenses for large sedan and electric vehicle (part 2)

For the large sedan, the cost per mile is $0.75$. For 30000 miles per year, the annual expense $L$ is $L = 30000\times0.75=22500$.
For the electric vehicle, with a cost per mile of $0.61$ and 30000 miles per year, the annual expense $E$ is $E = 30000\times0.61 = 18300$.
The annual difference $D$ is $D=22500 - 18300=4200$.
Over 6 years, the total difference $T$ is $T = 4200\times6=25200$

Answer:

a. The total annual expense for an electric vehicle is $\$8540$.
b. The amount saved at the end of six years is approximately $\$56028.38$.

1. The total annual expense for a large sedan exceeds that of an electric vehicle by $\$25200$ over six years.