Answer :
Answer:
the amount in the account at the end of 1 year will be;
[tex]\text{ \$3,}244.80[/tex]Explanation:
Given that Three thousand dollars is deposited at 8 percent interest compounded semiannually.
[tex]\begin{gathered} \text{ Principal P}=\text{ \$3,000} \\ \text{rate r = 8\% = 0.08} \\ \text{time t= 1 year} \\ \text{ number of times compounded n = 2 (semiannually)} \end{gathered}[/tex]The future value F of a compound interest can be calculated using the formula;
[tex]F=P(1+\frac{r}{n})^{nt}[/tex]Substituting the given values into the formula;
[tex]\begin{gathered} F=3,000(1+\frac{0.08}{2})^{2(1)} \\ F=3,000(1+0.04)^2 \\ F=3,000(1.04)^2 \\ F=3,000(1.0816) \\ F=3,244.80 \end{gathered}[/tex]Therefore, the amount in the account at the end of 1 year will be;
[tex]\text{ \$3,}244.80[/tex]