Amishi deposited $600, at the end of each six months for 18 years in a savings account. If the account paid 8% interest, compounded semiannually, use the appropriate formula to find the future value of her account. (Round your answer to the nearest cent.)

To find the future value of the account where equal payments are made at the end of each period for a specified number of periods, we can use the Future Value of an Ordinary Annuity formula:

[tex]FV=PMT\left[\dfrac{\left(\left(1+\dfrac{r}{t}\right)^{nt}-1\right)}{\dfrac{r}{t}}\right][/tex]

where:

FV = Future Value
PMT = Payment Amount
r = interest rate per year (decimal form)
n = number of times interest is applied per year
t = time in years

In this case:

PMT = $600
r = 8% = 0.08
n = 2 (semi-annually)
t = 18 years

Substitute the given values into the formula and solve for FV:

[tex]FV=600\left[\dfrac{\left(\left(1+\dfrac{0.08}{2}\right)^{2 \cdot 18}-1\right)}{\dfrac{0.08}{2}}\right]\\\\\\\\FV=600\left[\dfrac{\left(\left(1.04\right)^{36}-1\right)}{0.04}\right]\\\\\\\\FV=46558.98830...\\\\\\FV=\$46,558.99\; \sf (nearest\;cent)[/tex]

Therefore, the future value of the account rounded to the nearest cent is:

[tex]\Large\boxed{\boxed{\$46,558.99}}[/tex]