To solve for the compound interest semiannually:
[tex]A\text{ = P(1+}\frac{r}{n})^{nt}[/tex][tex]\begin{gathered} \text{ Principal = \$10,000} \\ \text{rate = 5\%} \\ time=\text{ 10years} \end{gathered}[/tex]First, convert R as a percent to r as a decimal
r = R/100
r = 5/100
r = 0.05 rate per year,
Then solve the equation for Amount = A, semiannually means twice in a year, n= 2
[tex]\begin{gathered} A\text{ = P(1+}\frac{r}{n})^{nt} \\ A=\text{ \$10000 (1+}\frac{0.05}{2})^{2(10)} \\ A=10000(1+0.025)^{20}\text{ } \\ A=10000(1.025)^{20} \\ A=\text{ \$10000(1.6386)} \\ A\text{ = \$16386} \end{gathered}[/tex]Therefore the annual interest compounded semiannually = $16386.95
Hence the correct answer is Option B
