Chapter 7.7, Problem 26E

To determine

To find: the percent of balance of the account change in the 5 years.

Answer to Problem 26E

  $21.67\%$ balance of the account change in 5 years.

Explanation of Solution

Given information: $P=\$1400,r=4\%\text{compounded}\text{annually},\text{and}t=5\text{years}$

Concept Used:

Compound interest problem requires the use of the following formula:

  $A=P{(1+\frac{r}{n})}^{nt}$

Calculation:

As per the given problem

  $P=\$1400,r=4\%\text{compounded}\text{annually},t=5\text{years}\text{and n=1 }$

Substitute the values in the formula

  $A=P{(1+\frac{r}{n})}^{nt}$

  $\Rightarrow A=1400{(1+\frac{0.04}{1})}^{1\times 5}$

  $\Rightarrow A=1400{(1.04)}^5$

  $\Rightarrow A=1703.31$

The balance of the account will be $\$1703.31$ after $5\text{years}$ .

Therefore,

  $\begin{array}{l}\text{percent}\text{increase}\text{in}\text{the}\text{balance}\text{after}\text{5}\text{years}=\frac{1703.31-1400}{1400}\times 100\\ \text{percent}\text{increase}\text{in}\text{the}\text{balance}\text{after}\text{5}\text{years}=21.67\%\end{array}$

Hence,

  $21.67\%$ balance of the account change in 5 years.

Conclusion:

  $21.67\%$ balance of the account change in 5 years.