Chapter 7.7, Problem 23PPS

To determine

Whether Brooke will have enough money for a trip to the Bahamas after 4 years.

Answer to Problem 23PPS

No.

Explanation of Solution

Given information:Brooke is saving money for a trip to the Bahamas that costs $295.99. She puts $150 into a savings account that pays 7.25% interest compounded quarterly.

Formula used:

Compound interest formula for compounded quarterly is given by,

  $A=P{(1+\frac{\raisebox{1ex}{$R$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}{100})}^{4t}$

where, $A=$ Amount

  $P=$ Principal

  $R=$ Rate % per annum

  $t=$ time

Calculation:

Here, $P=$ $150, $R=7.25\%$ , $t=4$ years.

Then, the amount after 4 years is given by,

  $A=P{(1+\frac{\raisebox{1ex}{$R$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}{100})}^{4t}$

  $\Rightarrow A=150{(1+\frac{\raisebox{1ex}{$7.25$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}{100})}^{4\cdot 4}$$\Rightarrow A=150{(1+\frac{7.25}{400})}^{16}$

  $\Rightarrow A={(\frac{407.25}{400})}^{16}$

  $\begin{array}{l}$ \Rightarrow A=150\times {(1.018125)}^{16}$\Rightarrow A=150\times 1.33296125\\ \Rightarrow A=199.944234\end{array}$

Rounding to nearest hundredths, $A=199.94$

After 4 years Brooke will get $199.94.

Thus, Brooke will not have enough money for a trip to Bahamas.