how much money should be deposited today in an account that earns 4% compounded semiannually so that it will…

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula for present value is $P = \frac{A}{(1+\frac{r}{n})^{nt}}$, where $A$ is the future value, $P$ is the present value, $r$ is the annual interest rate (in decimal form), $n$ is the number of times compounded per year, and $t$ is the number of years.

Step2: Convert the given values to the appropriate form

We have $A=$10000$, $r = 0.04$ (since $4%=0.04$), $n = 2$ (compounded semiannually), and $t = 3$ years.

Step3: Substitute the values into the formula

$P=\frac{10000}{(1 +\frac{0.04}{2})^{2\times3}}=\frac{10000}{(1 + 0.02)^{6}}$.

Step4: Calculate $(1 + 0.02)^{6}$

$(1 + 0.02)^{6}=1.02^{6}\approx1.126162$.

Step5: Calculate the present value $P$

$P=\frac{10000}{1.126162}\approx8884.87$.

Answer:

$8884.87$