Chapter MPS, Problem 7.9MPS

(a)

To determine

To Find: The future cost of the gas.

Answer to Problem 7.9MPS

  $\$7.64$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Current cost of a gallon of gas}=\$3.98\\ \text{Period}=6\text{months}\\ \text{Rate}=2.7\%\end{array}$

Formula Used:

  $\begin{array}{l}C=c{\left(1+r\right)}^n\\ C=\text{future cost}\\ c=c\text{urrrent cost}\\ n=\text{number of years}\\ r=\text{rate of inflation}\end{array}$

Calculation:

  $\begin{array}{l}\text{⇒}C=3.98{\left(1+2.7\right)}^{1/2}\\ \text{⇒}C=3.98{\left(3.7\right)}^{1/2}\\ \text{⇒}C=3.98\times 1.92\\ \text{⇒}C=\$7.64\end{array}$

Conclusion:

Thus the future cost of the gas is $\$7.64$ .

(b)

To determine

To Find: The future cost of the car.

Answer to Problem 7.9MPS

  $\$28565$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Current cost of a car}=\$14500\\ \text{Period}=6\text{months}\\ \text{Rate}=2.9\%\end{array}$

Formula Used:

  $\begin{array}{l}C=c{\left(1+r\right)}^n\\ C=\text{future cost}\\ c=c\text{urrrent cost}\\ n=\text{number of years}\\ r=\text{rate of inflation}\end{array}$

Calculation:

  $\begin{array}{l}\text{⇒}C=14500{\left(1+2.9\right)}^{1/2}\\ \text{⇒}C=14500{\left(3.9\right)}^{1/2}\\ \text{⇒}C=14500*1.97\\ \text{⇒}C=\$28565\end{array}$

Conclusion:

Thus the future cost of the car is $\$28565$