mishi deposited $$ \$ 800 $$, at the end of each six months for 18 years in a avings 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.)

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We first note that Mishi makes deposits at the end of every six‐month period for 18 years. Since there are 2 periods per year, the number of deposits (and compounding periods) is

$$
n = 18 \times 2 = 36.
$$

The annual interest rate is $$8\%$$ compounded semiannually, so the interest rate per period is

$$
i = \frac{8\%}{2} = 4\% = 0.04.
$$

For an annuity with deposits made at the end of each period, the future value $$S$$ is given by

$$
S = R \frac{(1+i)^n - 1}{i},
$$

where $$R$$ is the deposit amount. Here, $$R = \$800$$.

Substitute the values into the formula:

$$
S = 800 \frac{(1.04)^{36} - 1}{0.04}.
$$

Now, calculate $$(1.04)^{36}$$. Using a calculator,

$$
(1.04)^{36} \approx 4.106.
$$

So the expression becomes

$$
S \approx 800 \frac{4.106 - 1}{0.04} = 800 \frac{3.106}{0.04}.
$$

Divide $$3.106$$ by $$0.04$$:

$$
\frac{3.106}{0.04} \approx 77.65.
$$

Then multiply by $$800$$:

$$
S \approx 800 \times 77.65 \approx 62\,120.
$$

Rounded to the nearest cent, the future value of Mishi's account is $$\$62\,120.00$$.
The future value of Mishi's account is \$62,120.00.

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

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