Chapter 12, Problem 12STP

To determine

To find: Find the dollar value of the account rounded to nearest penny after $10$ years.

Answer to Problem 12STP

Final dollar value of amount $=A=780.25$

Explanation of Solution

Given information:

Principal value $=p=\$500$

Interest rate $=r=\frac{4.5}{100}=0.045$

Time $=t=10$ years.

  $n=2$ because it is compounded semiannually

Concept:

Final amount of Compound interest is

  $A=p{\left(1+\frac{r}{n}\right)}^{nt}$

Given

Principal value $=p=\$500$

Interest rate $=r=\frac{4.5}{100}=0.045$

Time $=t=10$ years.

  $n=2$ because it is compounded semiannually

We know

Final amount of Compound interest is

  $A=p{\left(1+\frac{r}{n}\right)}^{nt}$

On substituting values

We get

  $\begin{array}{l}A=p{\left(1+\frac{r}{n}\right)}^{nt}\\ \Rightarrow A=500{\left(1+\frac{0.045}{2}\right)}^{2\left(10\right)}\\ \Rightarrow A=500{\left(1+0.0225\right)}^{20}\\ \Rightarrow A=500{\left(1.0225\right)}^{20}\\ \Rightarrow A=500\left(1.5605092\right)\\ \Rightarrow A=780.25\end{array}$

Therefore,

Final dollar value of amount $=A=780.25$