Chapter 8.2, Problem 23PPS

To determine

To find: the balance in the account after $12$ years.

Answer to Problem 23PPS

The balance amount in the account after $12$ years is $\$97362.61$ .

Explanation of Solution

Given information:

The given data are given by,

  $\begin{array}{c}n=12\text{year}\\ v_0=\$21,000\\ i_a=13.2\%\end{array}$

The model formula for the ending value at time $n$ from the initial value at time $0$ is $v_n=v_0{\left(1+\frac{i_a}{p}\right)}^{np}$ .

Substitute $21,000$ for $v_0$ , $2$ for $p$ (for semi-annually), $12$ for $n$ , and $13.2\%$ for $i_a$ in the formula $v_n=v_0{\left(1+\frac{i_a}{p}\right)}^{np}$ to find the value of $a$ .

  $\begin{array}{c}{v}_{12}=21,000{\left(1+\frac{0.132}{2}\right)}^{12\times 2}\\ =21,000{\left(1.0066\right)}^{30}\\ =21,000\left(4.6363\right)\\ =97362.61\end{array}$

Therefore, the balance amount in the account after $12$ years is $\$97362.61$ .