Chapter 9.7, Problem 9PPS

To determine

Will she have enough money in the account after 4 years and Explain

Answer to Problem 9PPS

After 4 years she have $\$199.94$

She will not have enough money

Explanation of Solution

Given information:

Brooke is saving money for a trip to the Bahamas that costs $295.99 and she puts $150 into a saving account with the interest rate of 7.25% compounded quarterly

Concept used:

• The formula for compound interest: $A=P{\left(1+\frac{r}{n}\right)}^{nt}$
• Where
  $\begin{array}{l}A=\text{final}\text{amount}\\ P=\text{principal}\text{balance}\\ r=\text{rate}\text{of}\text{interest}\\ n=\text{number}\text{of}\text{times}\text{intrest}\text{applied}\text{per}\text{time}\text{period}\\ t=\text{number}\text{of}\text{time}\text{periods}\end{array}$

Calculation:

To find the value of his investment in 7 years

  $\begin{array}{c}P=\$150\\ r=7.25\text{\%}\\ \text{=}\frac{7.25}{100}\\ =0.0725\\ t=4\\ n=4\end{array}$

  $\begin{array}{l}A=P{\left(1+\frac{r}{n}\right)}^{nt}\\ A=150{\left(1+\frac{0.0725}{4}\right)}^{4\times 4}\\ =150{\left(1.0181\right)}^{16}\\ A=199.94\end{array}$

Thus, after 4 years she have $\$199.94$

She will not have enough money