how much money will there be in an account at...

# Explanation: ## Step1: Identify compound - interest formula The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal form), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years. ## Step2: Convert values to appropriate form Given $P=\$6000$, $r = 0.04$ (since $4\%=0.04$), $n = 2$ (compounded semiannually), and $t = 5$ years. ## Step3: Substitute values into formula $A=6000(1 +\frac{0.04}{2})^{2\times5}$. First, calculate the value inside the parentheses: $\frac{0.04}{2}=0.02$, and $1 + 0.02=1.02$. Then, calculate the exponent: $2\times5 = 10$. So, $A = 6000\times(1.02)^{10}$. ## Step4: Calculate $(1.02)^{10}$ Using a calculator, $(1.02)^{10}\approx1.21899442$. ## Step5: Calculate $A$ $A=6000\times1.21899442\approx7313.97$. # Answer: $\$7313.97$