Respuesta :
Solution:
The amount deposited is
[tex]=P[/tex]The number of times compounded is semi-annually, that is
[tex]n=2[/tex]The time t is
[tex]t=1[/tex]The rate at which P was compounded semi-annually is
[tex]r=8\%=0.08[/tex]The amount in the account after one year is
[tex]A=10,816[/tex]Concept:
The formula for compound interest is given below as
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]By substituting the values, we will have
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ 10,816=P(1+\frac{0.08}{2})^{2\times1} \\ 10,816=P(1+\frac{0.08}{2})^2 \\ \end{gathered}[/tex]By solving for the value of P, we will have
[tex]\begin{gathered} 10,816=P(1+\frac{0.08}{2})^2 \\ 10,816=P(1+0.04^{})^2 \\ 10,816=P(1.04)^2 \\ 10,816=P\times1.0816 \\ \text{divide both sides by 1.0816} \\ \frac{10,816}{1.0816}=\frac{P\times1.0816}{1.0816} \\ P=10,000 \end{gathered}[/tex]Hence,
The value of P = 10,000
