how much money will there be in an account at the end of 5 years if $6000 is deposited at 4% interest…

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$